{"id":2009,"date":"2022-01-30T15:00:43","date_gmt":"2022-01-30T15:00:43","guid":{"rendered":"https:\/\/cog-ist.com\/?post_type=blog_content&p=2009"},"modified":"2025-09-08T19:52:31","modified_gmt":"2025-09-08T19:52:31","slug":"bilissel-bilim-ne-kadar-zor-rich-haan-wareham-van-rooij","status":"publish","type":"blog_content","link":"https:\/\/cog-ist.com\/en\/blog_content\/bilissel-bilim-ne-kadar-zor-rich-haan-wareham-van-rooij\/","title":{"rendered":"Bili\u015fsel Bilim Ne Kadar Zor? \u2014 Rich, Haan, Wareham,\u00a0van Rooij"},"content":{"rendered":"\n

\u00d6zg\u00fcn Ad\u0131:\u00a0How hard is cognitive science?<\/a><\/p>\n\n\n\n

Patricia Rich<\/em><\/strong><\/p>\n\n\n\n

Felsefe B\u00f6l\u00fcm\u00fc, Bayreuth \u00dcniversitesi, Almanya<\/p>\n\n\n\n

Ronald de Haan<\/em><\/strong><\/p>\n\n\n\n

Mant\u0131k, Dil ve Hesaplama Enstit\u00fcs\u00fc, Amsterdam \u00dcniversitesi, Hollanda<\/p>\n\n\n\n

Todd Wareham<\/em><\/strong><\/p>\n\n\n\n

Bilgisayar Bilimi B\u00f6l\u00fcm\u00fc, Newfoundland Memorial \u00dcniversitesi, Kanada<\/p>\n\n\n\n

Iris van Rooij<\/em><\/strong><\/p>\n\n\n\n

Donders Beyin, Bili\u015f ve Davran\u0131\u015f Enstit\u00fcs\u00fc, Radboud \u00dcniversitesi, Hollanda<\/p>\n\n\n\n

Bili\u015fsel Bilim Ne Kadar Zor?<\/h1>\n\n\n\n

\u00d6Z<\/strong><\/h2>\n\n\n\n

Bili\u015fsel bilimin kendisi bili\u015fsel bir aktivitedir. Yine de, hesaplamal\u0131 bili\u015fsel bilim ara\u00e7lar\u0131 nadir olarak bili\u015fsel bilimcilerin d\u00fc\u015f\u00fcnmesini (s\u0131n\u0131rlar\u0131n\u0131) ara\u015ft\u0131r\u0131r. Burada, bunu hesaplama d\u00fczeyinde (computational-level<\/em>) modelleme ve karma\u015f\u0131kl\u0131k analizi (complexity analysis<\/em>) kullanarak ger\u00e7ekle\u015ftiriyoruz. Bili\u015fsel bilimcilerin kar\u015f\u0131la\u015ft\u0131\u011f\u0131 temel bir \u00e7\u0131kar\u0131m probleminin idealize edilmi\u015f bi\u00e7imsel bir modelini sunuyoruz: Bir sistemin davran\u0131\u015flar\u0131n\u0131n g\u00f6zlemlerinin verilmi\u015f oldu\u011fu bir durumda, bu davran\u0131\u015flar\u0131 makul bir bi\u00e7imde \u00fcretebilecek bili\u015fsel s\u00fcre\u00e7lerin \u00e7\u0131kar\u0131m\u0131. Bu problemin varyantlar\u0131n\u0131 farkl\u0131 a\u00e7\u0131klama seviyelerinde ele al\u0131yoruz ve her seviyede \u00e7\u0131kar\u0131m probleminin izlenemez (intractable<\/em>) ve hatta hesaplanamaz (uncomputable<\/em>) oldu\u011funu kan\u0131tl\u0131yoruz. Bu durumun bili\u015fsel bilim a\u00e7\u0131s\u0131ndan ne ima etti\u011fini tart\u0131\u015f\u0131yoruz.<\/p>\n\n\n\n

Anahtar Kelimeler: <\/strong>bili\u015fsel bilim felsefesi, bi\u00e7imsel epistomoloji (formal epistemology<\/em>), d\u0131\u015fa\u00e7ekim (abduction<\/em>), hesaplamasal karma\u015f\u0131kl\u0131k (computational complexity<\/em>), izlenemezlik (intractability<\/em>)<\/p>\n\n\n\n

G\u0130R\u0130\u015e<\/strong><\/h2>\n\n\n\n

Bir bili\u015fsel sistemin davran\u0131\u015f\u0131n\u0131 ve i\u00e7sel mekanizmas\u0131n\u0131 a\u00e7\u0131klamak isteyen, Dr. Conjectura isimli bir bilim insan\u0131 hayal edin. Girdi-\u00e7\u0131kt\u0131 davran\u0131\u015flar\u0131n\u0131n \u00fcst d\u00fczey (high-level<\/em>) fonksiyonel a\u00e7\u0131klamalar\u0131ndan d\u00fc\u015f\u00fck d\u00fczeyli i\u015flem (lower-level process<\/em>) ya da mekanik a\u00e7\u0131klamalar\u0131na uzanan farkl\u0131 anlamsal birim (granularity<\/em>) d\u00fczeylerindeki a\u00e7\u0131klamalarla ilgileniyor olabilir [1] [2] [3] [4] [5] [6]. Dr. Conjectura\u2019n\u0131n kar\u015f\u0131 kar\u015f\u0131ya oldu\u011fu birtak\u0131m zorluklar \u015fimdiye kadar fark edilmi\u015f ve \u00e7e\u015fitli seviyelerde \u00e7al\u0131\u015f\u0131lm\u0131\u015ft\u0131r. Geleneksel olarak, belirsizli\u011fin olu\u015fturdu\u011fu zorluklar odak noktas\u0131 olmu\u015ftur (\u00f6r. veriden istatistiksel \u00e7\u0131kar\u0131m etkileri [statistically inferring effects from data<\/em>], t\u00fcmevar\u0131m problemleri ve genellenebilirlik, verilere g\u00f6re teoride eksik belirlenim [underdetermination<\/em>]). Bu yaz\u0131da biz, t\u00fcm bu belirsizli\u011fin ortadan kald\u0131r\u0131lm\u0131\u015f olmas\u0131 halinde bile, bili\u015fi a\u00e7\u0131klayabilmenin \u00f6n\u00fcnde b\u00fcy\u00fck bir engel kalaca\u011f\u0131n\u0131 g\u00f6steriyoruz. Bilhassa, Dr. Conjectura\u2019n\u0131n \u00e7\u00f6zmeyi ama\u00e7lad\u0131\u011f\u0131 \u00e7\u0131kar\u0131m problemleri (inference problems<\/em>) hesaplamasal olarak izlenemezler (computationally intractable<\/em>) ve hatta baz\u0131lar\u0131 hesaplanamazd\u0131r. Bu da bize, yaln\u0131zca belirsizli\u011fi (uncertanity<\/em>) ortadan kald\u0131rmak veya yan\u0131tlamak i\u00e7in kullan\u0131lan tekniklerle bili\u015fi a\u00e7\u0131klayamayaca\u011f\u0131m\u0131z\u0131 g\u00f6sterir; bu g\u00f6rev daha temel bir bi\u00e7imde zordur ve farkl\u0131 t\u00fcr stratejiler gerektirir.<\/p>\n\n\n\n

Enerjinin \u00e7o\u011funun nereye harcand\u0131\u011f\u0131na dayanarak, bili\u015fsel biliminin ba\u015fl\u0131ca zorlu\u011funun yeterli ve y\u00fcksek kaliteli ampirik delillerin toplanmas\u0131 oldu\u011fu s\u00f6ylenebilir. Bu fikir, (b\u00fcy\u00fck \u00f6l\u00e7\u00fcde \u201ctekrarlanabilirlik krizi\u201d ile (replication crisis<\/em>) ortaya \u00e7\u0131km\u0131\u015f olan) g\u00fcncel bilimsel reformlar\u0131n hangi etkilerin ger\u00e7ek, hangilerinin hayali oldu\u011fuyla ilgili belirsizli\u011fi azaltmaya y\u00f6nelik uygulamalar ve prosed\u00fcrler tasarlamaya odaklanm\u0131\u015f olmas\u0131 ger\u00e7e\u011fiyle daha da g\u00fc\u00e7lendirilebilir [7] [8]. Bu yakla\u015f\u0131mlar\u0131n yard\u0131mc\u0131 m\u0131 oldu\u011fu yoksa engel mi olu\u015fturdu\u011fu tart\u0131\u015fma konusudur [9] [10] [11], fakat tart\u0131\u015fman\u0131n seyri ad\u0131na bu zorlu\u011fun \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fcn\u00fc ve deneylerimizin ve istatistiksel analizlerimizin sadece ger\u00e7ek sonu\u00e7lar\u0131 ortaya koyaca\u011f\u0131n\u0131 varsayal\u0131m. Ancak h\u00e2l\u00e2, mevcut sonu\u00e7lar\u0131n gelecek g\u00f6zlemlere dair \u00e7\u0131kar\u0131m yapmadaki yetersizli\u011finden kaynaklanan b\u00fcy\u00fck bir problem mevcuttur: t\u00fcmevar\u0131m problemi [12] [13]. Dr. Conjectura, insanlar\u0131n belirli bir \u015fekilde davrand\u0131\u011f\u0131n\u0131 ya da bir deney s\u0131ras\u0131nda beyinde belirli bir b\u00f6lgenin aktive oldu\u011funu g\u00f6zlemlemi\u015f, ama bu g\u00f6zlemleri ba\u011flamlar ve zamanlar baz\u0131nda nas\u0131l genelleyece\u011fiyle ilgili karars\u0131z kalm\u0131\u015f olabilir.<\/p>\n\n\n\n

Fakat t\u00fcmevar\u0131m probleminin de (the problem of induction<\/em>) \u00e7\u00f6z\u00fcld\u00fc\u011f\u00fcn\u00fc ve hatta Dr. Conjectura\u2019n\u0131n \u015fimdi ve gelecekteki t\u00fcm ger\u00e7eklere tam ve otomatik eri\u015fiminin oldu\u011funu varsayal\u0131m. Bu durumda tahminleri do\u011fru olurdu, ancak Dr. Conjectura bize bili\u015fsel fenomenlerin do\u011fru a\u00e7\u0131klamalar\u0131n\u0131 da sa\u011flayabilir miydi? Geriye az bir i\u015f kalm\u0131\u015f gibi g\u00f6r\u00fcnebilir ama a\u00e7\u0131klama h\u00e2l\u00e2 eksiktir. Hem b\u00fcy\u00fck miktarda veri pratik bir zorluk yarat\u0131r, hem de teori, veriler taraf\u0131ndan (herkes\u00e7e bilinen \u015fekilde) eksik belirlenmi\u015f olur [14]. Dr. Conjectura, bu yeni teori tarafs\u0131z oldu\u011fu i\u00e7in daha do\u011fru oldu\u011fundan de\u011fil, daha basit ve i\u015fe yarar oldu\u011fu i\u00e7in gelecekteki g\u00f6zlemcilerin teoriyi daha uygun bir alternatif ile de\u011fi\u015ftirmeleri i\u00e7in bir a\u00e7\u0131klama sunmu\u015f olabilir [17].<\/p>\n\n\n\n

\u015eimdi, bu zorlu\u011fun da ortadan kalkt\u0131\u011f\u0131n\u0131 varsayal\u0131m; bir \u015fekilde kesin olarak biliyoruz ki, kabul edilebilir tek bir teori verimizle tutarl\u0131d\u0131r. Bir\u00e7o\u011funun, geride ciddi teorik zorluklar kalmad\u0131\u011f\u0131n\u0131 ve Dr. Conjectura\u2019n\u0131n art\u0131k isteyebilece\u011fimiz t\u00fcm cevaplar\u0131 bize kesin olarak sa\u011flayabilece\u011fini d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcn\u00fc farz ediyoruz. Bu makalenin amac\u0131, bunun do\u011fru olmad\u0131\u011f\u0131n\u0131 kan\u0131tlamakt\u0131r: Bilimsel \u00e7\u0131kar\u0131m problemlerinden t\u00fcm belirsizlikler kald\u0131r\u0131lm\u0131\u015f olsa bile, a\u00e7\u0131klamalar \u00fcretebilmenin \u00f6n\u00fcnde \u00e7\u0131kar\u0131m problemlerinin hesaplama karma\u015f\u0131kl\u0131\u011f\u0131ndan kaynakl\u0131 ilkesel engeller bulunmaktad\u0131r. Bu \u00e7\u0131kar\u0131m problemlerimizin, cevaplar\u0131m\u0131z\u0131n tamam\u0131yla belirsizli\u011fe (uncertainty<\/em>) y\u00f6nelik olarak geli\u015ftirilmesiyle \u00e7\u00f6z\u00fclemeyece\u011fini g\u00f6stermektedir. Dahas\u0131, bilimsel \u00e7\u0131kar\u0131m\u0131n \u00f6n\u00fcndeki hesaplama engellerine y\u00f6nelik stratejiler bulmay\u0131 d\u00fc\u015f\u00fcnmenin di\u011fer engeller ele al\u0131nd\u0131ktan sonraya ertelenmesi de bir hata olu\u015fturmaktad\u0131r; Dr. Conjectura uzun vadede ba\u015far\u0131ya g\u00f6t\u00fcrmeyecek olan k\u0131sa vadeli \u00e7\u00f6z\u00fcmlerle vakit kaybetmediyse, metodolojik \u00f6neriler, her \u015feyin d\u00fc\u015f\u00fcn\u00fcld\u00fc\u011f\u00fc olas\u0131 ihtimaller a\u00e7\u0131s\u0131ndan de\u011ferlendirilmelidir.<\/p>\n\n\n\n

Makalenin geri kalan\u0131 \u015fu \u015fekilde organize edilmi\u015ftir. \u0130lk olarak, Dr. Conjectura\u2019n\u0131n bir bili\u015fsel sistemin i\u015fleyi\u015fiyle ilgili a\u00e7\u0131klamalar \u00fcretirken kar\u015f\u0131la\u015ft\u0131\u011f\u0131 \u00e7\u0131kar\u0131m problemlerinin idealle\u015ftirilmi\u015f modellerini sunaca\u011f\u0131z. Sonras\u0131nda, bu \u00e7\u0131kar\u0131m problemlerinin ne kadar zor olduklar\u0131n\u0131, hesaplamasal ve karma\u015f\u0131k matematik teorilerinin kavramlar\u0131n\u0131, ara\u00e7lar\u0131n\u0131 ve tekniklerini kullanarak analiz edece\u011fiz. Son olarak, h\u00e2lihaz\u0131rda var olan \u00e7al\u0131\u015fmalara g\u00f6re sonu\u00e7lar\u0131m\u0131z\u0131 konumland\u0131raca\u011f\u0131z ve sonu\u00e7lar\u0131m\u0131z\u0131n bili\u015fsel bilimcilerin kullan\u0131m\u0131na y\u00f6nelik etkilerini a\u00e7\u0131klamak i\u00e7in kurmaca bir diyalog kullanaca\u011f\u0131z.<\/p>\n\n\n\n

Bilimsel D\u0131\u015fa\u00e7ekimsel \u00c7\u0131kar\u0131mlar\u0131n Bi\u00e7imselle\u015ftirilmesi<\/strong><\/h2>\n\n\n\n

Bu b\u00f6l\u00fcmde, Dr. Conjectura\u2019n\u0131n bir bili\u015fsel sistem olan M<\/em>\u2019nin (bkz. \u015eekil 1) i\u015fleyi\u015fini a\u00e7\u0131klamaya \u00e7al\u0131\u015f\u0131rken kar\u015f\u0131la\u015ft\u0131\u011f\u0131 \u00e7\u0131kar\u0131m problemlerini bi\u00e7imle\u015ftirece\u011fiz. Genellik\u2019i (generality<\/em>) kaybetmeden, olduk\u00e7a idealle\u015ftirilmi\u015f bir senaryoyla \u00e7al\u0131\u015f\u0131yoruz: Dr. Conjectura\u2019n\u0131n, hi\u00e7bir g\u00f6zlemde \u00f6l\u00e7\u00fcm veya yorumlama hatas\u0131n\u0131n bulunmad\u0131\u011f\u0131 D\u2286 S \u00d7 B <\/em>veri setine eri\u015fimi bulunmaktad\u0131r. Her \u00e7ift (s, b<\/em>) \u2208 D<\/em>, M<\/em>\u2019nin bir durumdaki (s <\/em>\u2208 S<\/em>) <\/em>g\u00f6zlemlenmi\u015f bir davran\u0131\u015f\u0131n\u0131 (b <\/em>\u2208 B<\/em>) <\/em>ifade etmektedir (bkz. Tablo 1).<\/p>\n\n\n\n

Tablo 1: Varsay\u0131msal veri seti D<\/em>\u2019nin \u00f6rneklemesi. Burada, durumlar herhangi bir \u015fey olabilir (\u00f6r. se\u00e7im problemleri, g\u00f6rsel g\u00f6revler, sosyal durumlar veya bunlar\u0131n kombinasyonlar\u0131). Ayn\u0131 \u015fekilde davran\u0131\u015flar da herhangi bir \u015fey olabilir (\u00f6r. se\u00e7imler, hareket y\u00f6r\u00fcngeleri, s\u00f6z eylemleri, reaksiyon s\u00fcreleri veya bunlar\u0131n kombinasyonlar\u0131).<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

Dr. Conjectura, D<\/em>\u2019den, <\/em>di\u011fer bir deyi\u015fle d\u0131\u015fa\u00e7ekimsel gidimsel \u00e7\u0131kar\u0131mlardan (abductive inference<\/em>) yola \u00e7\u0131karak, d\u00fcnyan\u0131n do\u011fas\u0131 ile ilgili art alan bilgisi (background knowledge<\/em>) (\u00f6r. hesaplama zaman al\u0131r, fiziksel sistemler mekanla s\u0131n\u0131rl\u0131d\u0131r) ve varsay\u0131mlar\u0131 da hesaba katarak, M<\/em> i\u00e7in fonksiyonel ve\/ya algoritmik seviyede a\u00e7\u0131klamalar \u00fcretmeyi hedeflemektedir. Biz bu fikri \u015fu \u015fekilde bi\u00e7imselle\u015ftiriyoruz: Dr. Conjectura, fonksiyonel seviyede bir a\u00e7\u0131klama olarak bir fonksiyon F\u2208<\/em> F arar; F fonksiyonlar s\u0131n\u0131f\u0131 (class of functions<\/em>) olmak \u00fczere F : S \u2192 2B <\/em>art alan varsay\u0131mlar\u0131n\u0131 kar\u015f\u0131lar.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

\u015eekil 1: Bir (bili\u015fsel) sistem olan M, <\/em>bilinmeyen bir FM <\/em>fonksiyonunu bilinmeyen bir AM<\/em> algoritmas\u0131 kullanarak hesapl\u0131yor. Dr. Conjectura M<\/em>\u2019nin davran\u0131\u015flar\u0131n\u0131 \u00e7e\u015fitli durumlarda g\u00f6zlemliyor ve g\u00f6zlemler ve art alan bilgisiyle (background knowledge<\/em>) tutarl\u0131 bir fonksiyon F<\/em> ve algoritma A <\/em>bulmaya \u00e7al\u0131\u015f\u0131yor. [Resim freepik.com adresinden \u00f6gelerle olu\u015fturulmu\u015ftur]<\/p>\n\n\n\n

Benzer bi\u00e7imde, Dr. Conjectura, A<\/em><\/strong>\u2019n\u0131n <\/em>algoritmalar s\u0131n\u0131f\u0131n\u0131 g\u00f6sterdi\u011fi ve ilgili art alan varsay\u0131mlar\u0131 kar\u015f\u0131layacak \u015fekilde F \u2208 <\/em>F<\/em><\/strong> fonksiyonunu hesaplayabildi\u011fi bir A\u2208<\/em> A<\/em><\/strong> algoritmas\u0131n\u0131 algoritmik seviyede a\u00e7\u0131klamaya \u00e7al\u0131\u015f\u0131r.<\/p>\n\n\n\n

Dr. Conjectura, bir \u015fekilde bu F <\/em>ve A <\/em>a\u00e7\u0131klamalar\u0131n\u0131, muhtemelen do\u011fal dil (natural language<\/em>), matematiksel g\u00f6sterim ve \u015fematik krokilerden faydalanarak tan\u0131mlamaya ihtiya\u00e7 duyacakt\u0131r [18] [19]. Dr. Conjectura\u2019n\u0131n fonksiyonel seviyede a\u00e7\u0131klamalar i\u00e7in kulland\u0131\u011f\u0131 bilimsel dil sistemini, herhangi bir LF<\/em> dizisini (bir fonksiyonun tan\u0131m\u0131) haritaland\u0131rabilen bir LF <\/em>fonksiyonu ve k\u00fcmeler S <\/em>ve B<\/em> olmak \u00fczere, bir LF <\/em>(S, B, LF<\/em>) = F : S \u2192<\/em> 2B<\/em> fonksiyonu olarak bi\u00e7imlendiriyoruz. Pratikte, bu t\u00fcr tan\u0131mlamalar geli\u015fig\u00fczel uzunlukta yap\u0131lamazlar; bilimsel bir makale ya da kitaba uygun uzunlukta olmalar\u0131 gerekir. Bu sebeple, biz Dr. Conjectura\u2019n\u0131n \u00e7al\u0131\u015f\u0131labilir ve yay\u0131nlanabilir olarak de\u011ferlendirdi\u011fi tan\u0131mlamalar\u0131n uzunlu\u011funda bir \u00fcst s\u0131n\u0131r (K<\/em>) varsay\u0131yoruz.<\/p>\n\n\n\n

\u015eu ana kadar elimizde olan bi\u00e7imlemelerle art\u0131k, Dr. Conjectura\u2019n\u0131n fonksiyonel seviyedeki a\u00e7\u0131klamalarla birlikte ortaya \u00e7\u0131kt\u0131k\u00e7a \u00e7\u00f6zd\u00fc\u011f\u00fc \u00e7\u0131kar\u0131m problemlerini daha kesin bir bi\u00e7imde tan\u0131mlayabiliriz (algoritmik seviye varyant\u0131n\u0131 ilerde ele alaca\u011f\u0131z):<\/p>\n\n\n\n

(F , LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIMLAR (ABDUCTIVE INFERENCE)<\/p>\n\n\n\n

Verilen: <\/em>G\u00f6zlemlenmi\u015f durum-davran\u0131\u015f ikilileriyle (s, b<\/em>) \u2208 S <\/em>\u00d7 B<\/em>, bilinmeyen bir F tipi FM<\/em> : SM <\/em>\u2192 2BM fonksiyonuyla birlikte, S <\/em>\u2286 SM<\/em>, B <\/em>\u2286 BM <\/em>ve \u00fcst s\u0131n\u0131r\u0131n K <\/em>\u2208 \u2115 \u222a {\u221e} oldu\u011fu bir D<\/em> veri seti.<\/p>\n\n\n\n

\u00c7\u0131kar\u0131m: D <\/em>ile tutarl\u0131<\/em> F <\/em>\u2208 F fonksiyonunun LF <\/em>\u2208 LF <\/em>tan\u0131m\u0131, \u00f6yle ki, b\u00f6yle bir LF<\/em>\u2019in varl\u0131\u011f\u0131 halinde LF<\/em> en fazla K <\/em>uzunlu\u011funda. Aksi halde \u201chi\u00e7\u201d.<\/p>\n\n\n\n

Burada \u2018tutarl\u0131\u2019dan kast\u0131n ne oldu\u011fu bir dereceye kadar yoruma a\u00e7\u0131kt\u0131r ve t\u0131pk\u0131 farkl\u0131 F<\/em><\/strong> s\u0131n\u0131flar\u0131nda ve LF<\/em> dillerinde oldu\u011fu gibi farkl\u0131 yorumlardan \u00e7\u0131kar\u0131m problemlerinin nispeten farkl\u0131 varyantlar\u0131 elde edilir. Sunumun kolayl\u0131\u011f\u0131n\u0131 sa\u011flamas\u0131 i\u00e7in, \u2018tutarl\u0131\u2019 kelimesini her bir (s, b<\/em>) \u2208 D<\/em> i\u00e7in b<\/em> \u2208 F <\/em>(s<\/em>) anlam\u0131nda kullanal\u0131m. Tart\u0131\u015fma b\u00f6l\u00fcm\u00fcnde a\u00e7\u0131klayaca\u011f\u0131m\u0131z gibi, analizlerimiz ve bulgular\u0131m\u0131z tan\u0131mdaki varyasyonlara kar\u015f\u0131 diren\u00e7lidir.<\/p>\n\n\n\n

D\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m problemini bir \u00f6rnekle a\u00e7\u0131kl\u0131yoruz: Diyelim ki Dr. Conjectura insanlar\u0131n se\u00e7im davran\u0131\u015f\u0131n\u0131 a\u00e7\u0131klamakla ilgileniyor. Bir meslekta\u015f\u0131, Dr. Mensura, Dr. Conjectura\u2019ya her ki\u015fiye se\u00e7imlerin (\u00f6r. ki\u015finin aralar\u0131ndan se\u00e7im yapabilece\u011fi se\u00e7enekler k\u00fcmesi) sunuldu\u011fu durumlar (s <\/em>\u2286 S) ve ki\u015finin yapm\u0131\u015f oldu\u011fu belirli bir se\u00e7im (b <\/em>\u2208 B) (verilen k\u00fcmeden se\u00e7ilmi\u015f bir veya daha fazla se\u00e7enek) olmak \u00fczere b\u00fcy\u00fck bir veri seti D <\/em>\u2286 S \u00d7 B sa\u011fl\u0131yor. \u00d6nceden alm\u0131\u015f olduklar\u0131 davran\u0131\u015fsal ekonomi e\u011fitimine dayanarak, Dr. Conjectura kat\u0131l\u0131mc\u0131n\u0131n davran\u0131\u015f\u0131n\u0131 tan\u0131mlayan fonksiyonel seviyedeki a\u00e7\u0131klaman\u0131n (LF<\/em>) takip eden sabitler (F ) ile olu\u015fturalaca\u011f\u0131n\u0131 varsaymaktad\u0131r: Her ki\u015finin (p)<\/em> se\u00e7im opsiyonlar\u0131n\u0131 (x <\/em>\u2208 X <\/em>) \u00f6znel de\u011ferle (up <\/em>(x<\/em>) \u2208 \u211d ) e\u015fle\u015ftiren bir kullan\u0131m i\u015flevi (up <\/em>(x) <\/em>\u2208 \u211d ) vard\u0131r ve ki\u015fi, baz\u0131 asgari \u00f6znel de\u011fer \u00f6l\u00e7\u00fctlerini (t<\/em>) kar\u015f\u0131layabilmek i\u00e7in opsiyonlar se\u00e7er. Di\u011fer bir deyi\u015fle, ki\u015fi (p<\/em>), se\u00e7eneklerin bir alt k\u00fcmesi (X\u2019<\/em> \u2286 X ) olacak \u015fekilde, x <\/em>\u2208 { x <\/em>| x <\/em>\u2208 X\u2019<\/em> ve up <\/em>(x<\/em>) \u2265 t <\/em>} bir se\u00e7im yapacakt\u0131r. Bu varsay\u0131mla, D <\/em>de\u011feri i\u00e7in d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m problemi, D <\/em>ile tutarl\u0131 bir i\u015flevler (up<\/em>) ve de\u011ferler (tp<\/em>) kombinasyonu aramaya indirgenmektedir. Elbette bu a\u00e7\u0131klaman\u0131n ayn\u0131 zamanda bir \u015fekilde (LF i\u00e7inde, \u00f6r. yukar\u0131da bizim de kulland\u0131\u011f\u0131m\u0131z gibi do\u011fal dil ve formel g\u00f6sterimlerin bir kar\u0131\u015f\u0131m\u0131 kullan\u0131larak) tan\u0131mlanmas\u0131 ve kullan\u0131labilirli\u011fi a\u00e7\u0131s\u0131ndan \u00e7ok uzun olmamas\u0131 gerekmektedir.<\/p>\n\n\n\n

Bu, Dr. Conjectura\u2019n\u0131n F ile ilgili yapabilece\u011fi varsay\u0131mlardan sadece birine \u00f6rnektir. Buna ek varsay\u0131mlar da yapabilir (\u00f6r. kullan\u0131m i\u015flevlerinin ge\u00e7i\u015fkenlik (transitivity<\/em>) gibi rasyonalite ilkelerini kar\u015f\u0131lamas\u0131); \u00e7ok daha farkl\u0131 varsay\u0131mlarda da bulunabilir (\u00f6r. tercihlerin dinamik olarak yap\u0131land\u0131r\u0131l\u0131p herhangi bir se\u00e7enek-seviyesi kullan\u0131m i\u015flevi (option-level utility function<\/em>) ile tan\u0131mlanamamas\u0131 [20]); veya neredeyse hi\u00e7 varsay\u0131m yapmayabilir (\u00f6r. karar verme i\u015fleminin baz\u0131 (hesaplanabilir veya i\u015flenebilir) i\u015flevlerle a\u00e7\u0131klanabilir olmas\u0131 durumu gibi [21]. Bu durum, (F,LF ) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIMLAR\u2019\u0131n model uyumu (model fitting<\/em>) gibi dar kapsaml\u0131 veya model belirleme (model specification<\/em>) ya da teori olu\u015fumu (theory formation<\/em>) gibi geni\u015f kapsaml\u0131 olarak yorumlanabilece\u011fini g\u00f6sterir.<\/p>\n\n\n\n

Bir sonraki a\u015famada, Dr. Conjectura\u2019\u0131n d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m problemini algoritmik seviyede tan\u0131ml\u0131yoruz. Burada yine, \u00fcst (\u00f6r. bili\u015fsel) d\u00fczeyden d\u00fc\u015f\u00fck (n\u00f6ral) d\u00fczeye uzanan herhangi bir anlamsal birim (cognitive granularity<\/em>) seviyesindeki a\u00e7\u0131klamalar\u0131n ifade edilebilmesi i\u00e7in bir dile (LA) ihtiya\u00e7 duyulmaktad\u0131r. Bu dilin fonksiyonel-seviye dili (LF) ile temel farkl\u0131l\u0131\u011f\u0131, LA\u2019n\u0131n yap\u0131c\u0131 <\/em>(constructive<\/em>) olmas\u0131 gerekmesidir. \u00d6rne\u011fin LF, Dr. Conjectura\u2019n\u0131n, X<\/em> \u2018 se\u00e7enekler k\u00fcmesinin sunuldu\u011fu bir karar vericinin, bu x<\/em>\u2019e nas\u0131l ula\u015f\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131klamadan, herhangi bir x <\/em>\u2208 { x <\/em>| x <\/em>\u2208 X<\/em>\u2019 ve up <\/em>(x<\/em>) \u2265 t <\/em>} se\u00e7ece\u011fini varsaymas\u0131na olanak tan\u0131m\u0131\u015ft\u0131r. Bunun aksine, bir ki\u015finin tam olarak nas\u0131l k\u00fcme \u00fcyeli\u011fini hesaplad\u0131\u011f\u0131n\u0131n <\/em>d\u00fc\u015f\u00fcn\u00fcld\u00fc\u011f\u00fcn\u00fc <\/em>algoritmik seviyede bir a\u00e7\u0131klaman\u0131n belirtmesi gerekmektedir. LA, yaln\u0131zca Dr. Conjectura\u2019\u0131n \u00e7al\u0131\u015f\u0131lan sistem taraf\u0131ndan ger\u00e7ekle\u015ftirilebilir oldu\u011funa inand\u0131\u011f\u0131 hesaplama ad\u0131mlar\u0131na izin veren bir programlama diline benzetilebilir. T\u0131pk\u0131 fonksiyonel seviye a\u00e7\u0131klamalar gibi, algoritmik seviye a\u00e7\u0131klamalar\u0131 yay\u0131nlanabilir olmal\u0131d\u0131r ve bu sebeple (\u00fczerinde hesaplama yapt\u0131klar\u0131 etki alanlar\u0131 sonsuz olmas\u0131na ra\u011fmen)geli\u015fig\u00fczel uzunlukta olamazlar. Dolay\u0131s\u0131yla, Dr. Conjectura\u2019\u0131n algoritmik seviyede a\u00e7\u0131klama problemini \u015fu \u015fekilde tan\u0131mlayabiliriz:<\/p>\n\n\n\n

(A, LA<\/em> ) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM<\/p>\n\n\n\n

Verilen: S <\/em>\u2286 SM<\/em>, B <\/em>\u2286 BM<\/em> ve \u00fcst s\u0131n\u0131r K <\/em>\u2208 \u2115 \u222a { \u221e } olmak \u00fczere, bilinmeyen bir A tipi algoritma AM<\/em> taraf\u0131ndan \u00fcretilmi\u015f, bilinmeyen bir FM <\/em>: SM <\/em>\u2192 2BM fonksiyonunu hesaplayan, g\u00f6zlemlenmi\u015f durum-davran\u0131\u015f ikilileri (s<\/em>, b<\/em>) \u2208 S <\/em>\u00d7 B <\/em>ile birlikte bir D<\/em> veri seti.<\/p>\n\n\n\n

\u00c7\u0131kar\u0131m: D <\/em>ile tutarl\u0131 <\/em>bir fonksiyon FA<\/em>\u2019y\u0131 hesaplayan bir algoritma A <\/em>\u2208 A\u2019n\u0131n tan\u0131m\u0131 LA<\/em> \u2208 LA, \u00f6yle ki, b\u00f6yle bir LA<\/em>\u2019n\u0131n var olmas\u0131 durumunda LA<\/em> en fazla K <\/em>uzunlu\u011funda. Aksi halde \u201chi\u00e7\u201d.<\/p>\n\n\n\n

(A, LA) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM ve (F, LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM\u2019\u0131n asl\u0131nda iki farkl\u0131 problem oldu\u011funu dikkate almak gerekmektedir; bunlardan biri i\u00e7in uygun olan \u00e7\u00f6z\u00fcm, otomatik olarak di\u011ferinin de \u00e7\u00f6z\u00fcm\u00fc olmaz. Tek y\u00f6nl\u00fc olarak bunu a\u00e7\u0131k\u00e7a g\u00f6rmek m\u00fcmk\u00fcnd\u00fcr: Bir F <\/em>fonksiyonunun LF<\/em> tan\u0131m\u0131, F<\/em>\u2019yi hesaplamak i\u00e7in bir A<\/em> algoritmas\u0131 belirtmez. Tersinin de ge\u00e7erli oldu\u011funu g\u00f6rebilmek i\u00e7in, A <\/em>algoritmas\u0131, LA <\/em>tan\u0131m\u0131n\u0131n F <\/em>fonksiyonunun hesaplanmas\u0131 i\u00e7in bir y\u00f6ntem belirleyebilirken, kendi i\u00e7inde LF<\/em> a\u00e7\u0131klay\u0131c\u0131 dilinde F<\/em>\u2019yi do\u011fal olarak k\u0131saca tan\u0131mlayamad\u0131\u011f\u0131n\u0131 unutmamak laz\u0131m [22] [23] [24].<\/p>\n\n\n\n

Hesaplamal\u0131 Karma\u015f\u0131kl\u0131k Analizi<\/strong><\/h2>\n\n\n\n

Dr. Conjectura\u2019ya y\u00f6neltilen \u00e7\u0131kar\u0131m problemlerinin ne kadar zor oldu\u011funu analiz etmek i\u00e7in hesaplama ve karma\u015f\u0131kl\u0131k matemati\u011finden kavramlar ve kan\u0131t tekniklerinden yola \u00e7\u0131kaca\u011f\u0131z. Ba\u015flang\u0131\u00e7 noktam\u0131z, anahtar tan\u0131mlar\u0131 ula\u015f\u0131labilir bir formda ama\u00e7lar\u0131m\u0131za yetecek bi\u00e7imde sunmak olacak. Daha kapsaml\u0131 ve formel i\u015fleyi\u015fler i\u00e7in \u015fu ders kitaplar\u0131 incelenebilir; [25] [26] [27] [28] [29].<\/p>\n\n\n\n

Tan\u0131m 1 (Hesaplanabilirlik) <\/strong>Bir ba\u011f\u0131nt\u0131n\u0131n (\u00f6r. fonksiyon veya \u00e7\u0131kar\u0131m problemi) Q<\/em> : X <\/em>\u2192 2Y<\/em>, her x <\/em>\u2208 X <\/em>i\u00e7in y <\/em>\u2208 Q <\/em>(x<\/em>)\u2019i hesaplayabilen en az bir algoritma olmas\u0131 halinde hesaplanabilir <\/em>oldu\u011fu s\u00f6ylenebilir. Aksi halde Q<\/em>\u2019nun hesaplanamaz <\/em>oldu\u011funu s\u00f6ylenir.<\/p>\n\n\n\n

Tan\u0131m 2 (P-Zaman Algoritmas\u0131)<\/strong> n<\/em> girdi boyutu ve c<\/em> sabit olmak \u00fczere O <\/em>(nc<\/em>) zaman\u0131nda y\u00fcr\u00fct\u00fclebilen bir A <\/em>algoritmas\u0131n\u0131n polinomsal zaman<\/em> (polynomial-time<\/em>) algoritmas\u0131 oldu\u011fu s\u00f6ylenebilir.<\/p>\n\n\n\n

\u00dcstel zaman (exponential time<\/em>) algoritmalar\u0131 gibi polinomsal zamandan daha uzun s\u00fcren algoritmalar genellikle, k\u00fc\u00e7\u00fck girdi boyutlar\u0131 haricinde, t\u00fcm girdi boyutlar\u0131 i\u00e7in izlenemez<\/em> olarak kabul edilir [30] [31]. Neden oldu\u011funu g\u00f6sterebilmek ad\u0131na, D<\/em> veri setiyle birlikte d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m problemini makul boyutta |D|<\/em>= 100 olarak hesaba katal\u0131m. Bu durumda, O <\/em>(cn<\/em>) zaman\u0131nda c <\/em>= 2 ile \u00e7al\u0131\u015fan bir \u00fcsl\u00fc zaman algoritmas\u0131, 1030 ad\u0131ml\u0131k mertebeler halini al\u0131r; bu da evrenin olu\u015fumundan bu yana ge\u00e7en saniye say\u0131s\u0131ndan (<1018 saniye) daha fazlad\u0131r. |D| <\/em>= 500 i\u00e7in bu say\u0131 10150\u2019luk bir mertebe olurdu ve evrendeki atom say\u0131s\u0131n\u0131 (< 1082 atom) ge\u00e7erdi. Bu da demektir ki, b\u00f6yle bir data grubu i\u00e7in bir beynin ya da makinenin\u2013ya da evrendeki b\u00fct\u00fcn atomlar kadar fazla paralel hesaplama kanallar\u0131 olan beyin ya da makinelerin birle\u015fiminin\u2013bu \u00e7\u0131kar\u0131msal s\u00fcreci tamamlamas\u0131 i\u00e7in evrenin olu\u015fumundan bu yana ge\u00e7en b\u00fct\u00fcn zaman kadar uzun bir s\u00fcrenin ge\u00e7mesi gerekir. \u015eu kadar\u0131 s\u00f6ylenilebilir ki, pratikte, izlenemez d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131mlar orta ile b\u00fcy\u00fck girdi boyutlar\u0131 i\u00e7in uygulanabilir de\u011fildir.<\/p>\n\n\n\n

Tan\u0131m 3 (\u0130zlenebilirlik) <\/strong>Bir Q<\/em> ba\u011f\u0131nt\u0131s\u0131n\u0131n, kendisini hesaplayabilecek en az bir polinomsal zaman algoritmas\u0131 olmas\u0131 halinde izlenebilir<\/em> oldu\u011fu s\u00f6ylenebilir. Aksi halde, Q<\/em> izlenemez.<\/em><\/p>\n\n\n\n

Tan\u0131m 4 (\u0130zlenebilir Do\u011frulanabilirlik) <\/strong>Bir Q <\/em>: X <\/em>\u2192 2Y<\/em> ba\u011f\u0131nt\u0131s\u0131n\u0131n, (i) x<\/em> boyutunda polinomsal zamanda y\u00fcr\u00fct\u00fclen bir algoritma olmas\u0131 ve (ii) verilen x <\/em>ve y<\/em>\u2019nin y <\/em>\u2208 Q <\/em>(x<\/em>) ge\u00e7erlili\u011fini do\u011frulayabilmesi halinde izlenebilir \u015fekilde do\u011frulanabilir<\/em> (tractably verifiable) <\/em>oldu\u011fu s\u00f6ylenebilir.<\/p>\n\n\n\n

E\u011fer Q<\/em> izlenebilir (tractable) ise, ayn\u0131 zamanda izlenebilir \u015fekilde do\u011frulanabilirdir (tractably verifiable). Bunun tam tersinin ise genel olarak yanl\u0131\u015f oldu\u011fu varsay\u0131l\u0131r [32].<\/p>\n\n\n\n

Burada, hem bili\u015fsel sistemler taraf\u0131ndan hesaplanan fonksiyonlar\u0131n hem de bili\u015fsel bilimcilerin kendilerinin \u00e7\u0131kar\u0131msal kapasitelerinin izlenebilirlik gereklilikleri ile s\u0131n\u0131rl\u0131 olduklar\u0131n\u0131 kabul ediyoruz (daha kapsaml\u0131 bir arg\u00fcman i\u00e7in bkz. [33]). Bu varsay\u0131ma dayanarak \u015fu soruyu soruyoruz: Bili\u015fsel bilim ne kadar zordur? Bu soruyu ele almak i\u00e7in, genel olarak Conjectura teoremleri <\/em>olarak bahsetti\u011fimiz bir dizi teori t\u00fcretiyoruz (bkz. detaylar ve ispatlar i\u00e7in ek materyaller ve genel bir bak\u0131\u015f i\u00e7in Tablo 2):<\/p>\n\n\n\n

Teorem 1 <\/strong>E\u011fer LF<\/em> \u2208 LF a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r yok ise (\u00f6r. K <\/em>= \u221e), bu durumda (F, LF) \u2013baz\u0131 LF i\u00e7in DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM hesaplanamaz.<\/p>\n\n\n\n

Teorem 1\u2019e g\u00f6re, LF izlenebilir olsa bile (ve dolay\u0131s\u0131yla F sadece izlenebilir fonksiyonlar i\u00e7erir.) ge\u00e7erlidir. Bu durum, (F, LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM\u2019\u0131n hesaplanamaz olu\u015funun sebebinin a\u00e7\u0131klanacak olan bili\u015fsel sistemin a\u015f\u0131r\u0131 karma\u015f\u0131k olmas\u0131ndan ziyade a\u00e7\u0131klaman\u0131n uzunlu\u011funda bir s\u0131n\u0131r bulunmamas\u0131ndan kaynaklan\u0131r. Bu yorum Teorem 2 ile do\u011frulanmaktad\u0131r.<\/p>\n\n\n\n

Teorem 2 <\/strong>E\u011fer LF<\/em> \u2208 LF a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r (K <\/em>\u2208 \u2115) var ise, bu durumda (F, LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM t\u00fcm LF i\u00e7in hesaplanabilir.<\/p>\n\n\n\n

Her ne kadar a\u00e7\u0131klamalar\u0131n uzunlu\u011fundaki s\u0131n\u0131rlar hesaplanabilirlik sa\u011flasa da, \u015fimdi g\u00f6sterilece\u011fi \u00fczere, hen\u00fcz izlenebilirlik (tractability) sa\u011flamamaktad\u0131r.<\/p>\n\n\n\n

Teorem 3 <\/strong>E\u011fer <\/strong>LF<\/em> \u2208 LF a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r (K <\/em>\u2208 \u2115) var ve LF izlenebilir (ve dolay\u0131s\u0131yla F yaln\u0131zca izlenebilir fonksiyonlar i\u00e7erir) ise bu durumda, (F, LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM baz\u0131 LF i\u00e7in izlenemezdir.<\/p>\n\n\n\n

Teorem 3, verilen herhangi bir veri seti i\u00e7in (s\u0131n\u0131rl\u0131 boyutlar\u0131 olan) izlenebilir fonksiyonel a\u00e7\u0131klamalar \u00fcretebilecek herhangi bir polinomsal zaman algoritmas\u0131n\u0131n var olamayaca\u011f\u0131n\u0131 g\u00f6stermektedir. M\u00fcmk\u00fcn olan \u015fey ise, \u015fimdi g\u00f6sterilece\u011fi \u00fczere, a\u00e7\u0131klamalar\u0131 tesad\u00fcfen bulundu\u011funda izlenebilir olarak tan\u0131makt\u0131r.<\/p>\n\n\n\n

Teorem 4 <\/strong>E\u011fer LF<\/em> \u2208 LF a\u00e7\u0131klamas\u0131n\u0131n bir s\u0131n\u0131r\u0131 (K <\/em>\u2208 \u2115) var ve LF izlenebilir (ve dolay\u0131s\u0131yla F yaln\u0131zca izlenebilir fonksiyonlar i\u00e7erir) ise bu durumda, (F, LF) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM t\u00fcm LF i\u00e7in izlenebilir \u015fekilde do\u011frulanabilirdir.<\/p>\n\n\n\n

M\u2019<\/em>nin sonlu durum otomat\u0131 (finite state automaton<\/em>) gibi s\u0131n\u0131rl\u0131 bir hesaplamal\u0131 arac\u0131 oldu\u011fu varsay\u0131ld\u0131\u011f\u0131nda bile Teorem 4 ge\u00e7erlidir.<\/p>\n\n\n\n

\u015eu ana kadar listelenen teoremler fonksiyonel seviyede a\u00e7\u0131klamalarla ilgidir. Algoritmik seviyede d\u0131\u015fa\u00e7ekimsele y\u00f6nelik de tamamen bunlarla benze\u015fik bir teoremler grubumuz bulunmaktad\u0131r.<\/p>\n\n\n\n

Teorem 5 <\/strong>E\u011fer <\/strong>LA<\/em> \u2208 LA a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r (\u00f6r. K <\/em>= \u221e) yoksa, bu durumda (A, LA) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM baz\u0131 LA i\u00e7in hesaplanamazd\u0131r.<\/p>\n\n\n\n

Teorem 6 <\/strong>E\u011fer LA<\/em> \u2208 LA a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011fundan bir s\u0131n\u0131r (K <\/em>\u2208 \u2115) varsa, bu durumda (A, LA ) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM t\u00fcm LA i\u00e7in hesaplanabilirdir.<\/p>\n\n\n\n

Teorem 7 <\/strong>E\u011fer LA<\/em> \u2208 LA a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r (K <\/em>\u2208 \u2115) varsa ve LA izlenebilir (dolay\u0131s\u0131yla A yaln\u0131zca izlenebilir fonksiyonlar i\u00e7erir) ise, bu durumda (A, LA ) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM baz\u0131 LA i\u00e7in izlenemezdir (intractable).<\/p>\n\n\n\n

Teorem 8 <\/strong>E\u011fer LA<\/em> \u2208 LA a\u00e7\u0131klamas\u0131n\u0131n uzunlu\u011funda bir s\u0131n\u0131r (K <\/em>\u2208 \u2115) varsa ve LA izlenebilir (dolay\u0131s\u0131yla A yaln\u0131zca izlenebilir fonksiyonlar i\u00e7erir) ise, bu durumda (A, LA) \u2014 DI\u015eA\u00c7EK\u0130MSEL \u00c7IKARIM t\u00fcm LA i\u00e7in izlenebilir \u015fekilde do\u011frulanabilirdir (tractably verifiable).<\/p>\n\n\n\n

Tart\u0131\u015fma<\/strong><\/h2>\n\n\n\n

Ara\u015ft\u0131rmam\u0131za, g\u00f6zlemlerimizde hi\u00e7bir belirsizlik olmasayd\u0131 ve ilgili t\u00fcm veriye eri\u015febiliyor olsayd\u0131k bili\u015fsel bilim ne kadar zor olurdu sorusunu sorarak ba\u015flad\u0131k. Conjectura teoremleri, b\u00f6yle ideal bir durumda bile g\u00f6zlemlerimizle tutarl\u0131 a\u00e7\u0131klamalar \u00fcretebilmenin, etkili herhangi bir d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m s\u00fcrecine kar\u015f\u0131 koydu\u011funu ortaya koymaktad\u0131r (sonu\u00e7lara genel bir bak\u0131\u015f i\u00e7in bkz. Tablo 2). Bulgular\u0131m\u0131z\u0131n etkilerini ortaya koymadan \u00f6nce onlar\u0131 literat\u00fcr \u00e7er\u00e7evesinde konumland\u0131r\u0131yoruz.<\/p>\n\n\n\n

Bili\u015fsel bilim camias\u0131n\u0131n bir k\u0131sm\u0131 bulgular\u0131n sezgilere ayk\u0131r\u0131 (unintuitive<\/em>) olduklar\u0131n\u0131 ve hayal k\u0131r\u0131kl\u0131\u011f\u0131 uyand\u0131rd\u0131klar\u0131n\u0131 d\u00fc\u015f\u00fcn\u00fcrken, di\u011ferleri \u015fa\u015f\u0131rmayacaklard\u0131r \u00e7\u00fcnk\u00fc en az\u0131ndan 1960\u2019lara dayanan ve \u00f6z\u00fcnde benzer sonu\u00e7lara sahip bir\u00e7ok negatif teorik sonu\u00e7 bulunmaktad\u0131r. G\u00f6ze \u00e7arpanlar\u0131n \u00e7o\u011funu, hesaplamal\u0131 ve klasik \u00f6\u011frenme teorisi [34] [35] [36] [37] ve bilimin bili\u015fsel bilimi olu\u015fturmaktad\u0131r [38]. Ara\u015ft\u0131rman\u0131n alanlar\u0131, ama\u00e7lar\u0131, genellenebilirlik dereceleri ve ele ald\u0131klar\u0131 bilimsel problemler farkl\u0131l\u0131k g\u00f6stermektedir. Bu var olan yakla\u015f\u0131mlarla bizim bi\u00e7imselle\u015ftirdi\u011fimiz aras\u0131nda birka\u00e7 \u00f6nemli fark bulunmaktad\u0131r.<\/p>\n\n\n\n

\"\"\/<\/figure>\n\n\n\n

\u00d6rne\u011fin; t\u00fcmevar\u0131m, tahmin etme veya test edilebilirlik yerine biz, a\u00e7\u0131klama yapmaya odaklan\u0131yoruz [39 [40]. S\u0131n\u0131rda \u00f6\u011frenilebilirlik (learnability in the limit<\/em>) [41] [42] yerine hesaplamal\u0131 karma\u015f\u0131kl\u0131\u011f\u0131 (computational complexity<\/em>) inceliyoruz. Daha genel bi\u00e7imselle\u015ftirmelerin [43] [44] tam tersine, bili\u015fsel sistemin art alan varsay\u0131mlar\u0131na dayanarak geri\u00e7\u0131kar\u0131m problemi \u00f6zelinde modelleme yap\u0131yoruz. Ancak modellerimiz, d\u0131\u015fa\u00e7ekimselin Bayes\u00e7i [45] [46] ya da tutarl\u0131 (coherentist<\/em>) [47] [48] modellerinin tam tersine, bili\u015fsel bilimdeki t\u00fcm a\u00e7\u0131klay\u0131c\u0131 hesaplamal\u0131 \u00e7er\u00e7eveleri kapsayacak kadar geneldir. \u00d6zetle, bi\u00e7imselle\u015ftirmelerimiz bili\u015fsel bilimcilerin ilgilendi\u011fi spesifik, tan\u0131mlanabilir d\u0131\u015fa\u00e7ekimsel \u00e7\u0131kar\u0131m problemlerinin ne kadar zor oldu\u011funu g\u00f6stermemize olanak sa\u011flamaktad\u0131r.<\/p>\n\n\n\n

Her ne kadar olumsuz sonu\u00e7lar\u0131n do\u011fas\u0131 gere\u011fi, \u00e7\u00f6z\u00fcmlemeden \u00e7evresinden dola\u015f\u0131lacak \u201c\u00e7\u00f6z\u00fcm\u201d olmasa da, hangi olumsuz sonu\u00e7lar\u0131n bu spesifik problemler i\u00e7in ge\u00e7erli oldu\u011funu belirtmek \u00f6nemlidir. Bunu, makine \u00f6\u011frenmesinin, \u00f6\u011frenme problemlerinin hepsine uygulanabilecek m\u00fckemmel bir algoritma yoktur [49] anlam\u0131na gelen \u201cbedava \u00f6\u011fle yeme\u011fi yok teoremi\u201d (no free lunch theorem<\/em>) ile kar\u015f\u0131la\u015ft\u0131ral\u0131m; bunun bilincinde olmak \u00f6nemlidir \u00e7\u00fcnk\u00fc b\u00f6ylece ara\u015ft\u0131rmac\u0131lar her \u015feye uygulanabilir en iyi algoritmay\u0131 bulmaya \u00e7al\u0131\u015fmazlar. Benzer \u015fekilde, t\u00fcm bili\u015fsel bilimcilerin de, her \u015feye en do\u011fru cevab\u0131 verecek bir genel s\u00fcrecin m\u00fcmk\u00fcn olmad\u0131\u011f\u0131n\u0131n ay\u0131rd\u0131na varmalar\u0131 \u00f6nemlidir \u00e7\u00fcnk\u00fc b\u00f6ylece, b\u00f6ylesi bir s\u00fcrece girmezler ve bu t\u00fcr bir sonucun varl\u0131\u011f\u0131n\u0131 iddia etmezler.<\/p>\n\n\n\n

Sonu\u00e7lar\u0131m\u0131z\u0131n bili\u015fsel bilimler ara\u015ft\u0131rma uygulamalar\u0131na olan etkilerinin t\u00fcm\u00fcn\u00fc ortaya d\u00f6kmek kolay de\u011fil ve bu yaz\u0131y\u0131 okuyanlar\u0131n her t\u00fcrl\u00fc soruya, itiraza ve kar\u015f\u0131t-sezgiselliklere (counter-intuition<\/em>) sahip olabileceklerini olabilece\u011fini d\u00fc\u015f\u00fcn\u00fcyoruz. Alan s\u0131n\u0131rl\u0131l\u0131\u011f\u0131 sebebiyle burada hepsine yer vermemiz m\u00fcmk\u00fcn de\u011fil. Bunun yerine bulgular\u0131n etkilerini, en muhtemel kayg\u0131lar\u0131 ele alarak kurgusal bir diyalogla ortaya koyaca\u011f\u0131z. Diyalogda, Dr. Conjectura (C <\/strong>ile ifade edilmi\u015f) sonu\u00e7lar\u0131n kendi uygulamalar\u0131 ile ilgisini g\u00f6rmeyen ku\u015fkucu rol\u00fcn\u00fc \u00fcstlenirken, R <\/strong>bizim cevaplar\u0131m\u0131z\u0131 yans\u0131tacakt\u0131r.<\/p>\n\n\n\n

C: <\/strong>Ara\u015ft\u0131rmam\u0131n amac\u0131na ula\u015fmak i\u00e7in bana yard\u0131m etmeye \u00e7al\u0131\u015fman\u0131z\u0131 takdir ediyorum ama bunu nas\u0131l ba\u015faraca\u011f\u0131n\u0131z\u0131 anlayam\u0131yorum. Bu teoremlerle benim ilgim nedir? Benim verilerim hi\u00e7bir zaman teorem olacak kadar ideal sonu\u00e7lar vermedi.<\/p>\n\n\n\n

R: <\/strong>Hangi ideal sonu\u00e7?<\/p>\n\n\n\n

C: <\/strong>M\u00fckemmel, hatas\u0131z g\u00f6zlemlerim oldu\u011funu varsayarak \u00e7\u0131kar\u0131m problemlerimi bi\u00e7imselle\u015ftirdiniz ancak verilerim hep eksik ve yanl\u0131\u015f sonu\u00e7lardan olu\u015fuyor.<\/p>\n\n\n\n

R: <\/strong>Teoremler, ideal durumda ger\u00e7eklerle tutarl\u0131 a\u00e7\u0131klamalar bulabilmenin izlenemez oldu\u011funu g\u00f6steriyor. \u0130lgili ger\u00e7eklerle ili\u015fkili daha \u00e7ok belirsizlik, bu problemi nas\u0131l daha kolay <\/em>hale getirebilir? Sadece daha zor <\/em>hale getirebilirmi\u015f gibi duruyor.<\/p>\n\n\n\n

C: <\/strong>Mant\u0131kl\u0131. Ama siz a\u00e7\u0131klamalar i\u00e7in ger\u00e7ek\u00e7i olmayan standartlar olu\u015fturdunuz. Hi\u00e7bir a\u00e7\u0131klama m\u00fckemmel de\u011fildir; en iyi ihtimalle m\u00fckemmele yak\u0131n olabilir.<\/p>\n\n\n\n

R: <\/strong>\u2018Yak\u0131nl\u0131k\u2019 derken tam olarak neyi kast ediyorsunuz?<\/p>\n\n\n\n

C: <\/strong>Mesela, a\u00e7\u0131klamalar\u0131n her zaman t\u00fcm <\/em>verilerle tutarl\u0131 olmas\u0131 gerekmiyor.<\/p>\n\n\n\n

R: <\/strong>Bu \u015fekilde y\u00fcksek bir standart varsaymam\u0131z gerekmiyor. A\u00e7\u0131klaman\u0131n, verinin yar\u0131s\u0131yla diyelim, tutarl\u0131 olmas\u0131 gerekse bile, b\u00f6yle \u2018yar\u0131-tutarl\u0131\u2019 a\u00e7\u0131klamalar \u00fcretebilmek yine de izlenemez (intractable<\/em>) olurdu.<\/p>\n\n\n\n

C: <\/strong>Oh. Bu kar\u015f\u0131t-sezgisel (counter-intuitive<\/em>).<\/p>\n\n\n\n

R: <\/strong>Umar\u0131m bu, tan\u0131tt\u0131\u011f\u0131m\u0131z idealizasyonlarla ilgili kayg\u0131lar\u0131n\u0131 ortadan kald\u0131rm\u0131\u015ft\u0131r. Genel olarak, \u00e7\u00f6z\u00fclmesi izlenemez olan \u00e7o\u011fu problemin ayn\u0131 zamanda, \u2018yak\u0131nl\u0131k\u2019 kelimesinin \u00e7e\u015fitli anlamlar\u0131 i\u00e7in, yak\u0131n olarak da \u00e7\u00f6z\u00fclmesi zordur.<\/p>\n\n\n\n

C: <\/strong>Ama ben h\u00e2l\u00e2 anlam\u0131yorum. E\u011fer bana m\u00fckemmel, hatas\u0131z g\u00f6zlemler veriyorsan\u0131z, benim i\u00e7in bu veri \u00fcreten mekanizmay\u0131 anlamam\u0131n kolay olmas\u0131 gerekmez mi?<\/p>\n\n\n\n

R: <\/strong>A\u00e7\u0131klama bir bedel olmaks\u0131z\u0131n gelmiyor. Dil ve matematikle tarifini yapabilece\u011finiz <\/em>olas\u0131 mekanizmalar\u0131n say\u0131s\u0131 astronomik d\u00fczeydedir. Verilerle tutarl\u0131 bir mekanizmay\u0131 saptayan bir a\u00e7\u0131klama bulmak samanl\u0131kta i\u011fne aramaya benzer; bu yeri arayacak etkili genel bir s\u00fcre\u00e7 yoktur.<\/p>\n\n\n\n

C: <\/strong>Ama ben h\u00e2lihaz\u0131rda se\u00e7enekleri daraltt\u0131m. Sadece spesifik bir bili\u015fsel yap\u0131 [buraya favori \u00e7er\u00e7evenizi girin, \u00f6r. ACT-R, Uyarlanabilir Ara\u00e7 Kutusu [Adaptive Toolbox], PDP, Subsumption-Architecture, vb.] i\u00e7in a\u00e7\u0131klama aray\u0131\u015f\u0131nday\u0131m.<\/p>\n\n\n\n

R: <\/strong>Sizin yap\u0131sal ba\u011fl\u0131l\u0131klar\u0131n\u0131za dayanarak uygun bi\u00e7imde, analizlerimiz bir se\u00e7enek olarak, olas\u0131 fonksiyonlar\u0131n (F k\u00fcmesi) alan\u0131n\u0131 ve algoritmalar\u0131n\u0131 (A) s\u0131n\u0131rland\u0131rarak bu bak\u0131\u015f\u0131 da kaps\u0131yor. Bu genel a priori <\/em>ba\u011fl\u0131l\u0131klarla bile, alan, \u00f6nemli \u00f6l\u00e7\u00fcde hesaplama g\u00fcc\u00fc olan yap\u0131lar i\u00e7in h\u00e2l\u00e2 astronomik \u00f6l\u00e7\u00fcde b\u00fcy\u00fck olmaya devam ediyor.<\/p>\n\n\n\n

C:<\/strong> <\/em>\u00d6nemli \u00f6l\u00e7\u00fcde derken neyi kast ediyorsunuz?<\/p>\n\n\n\n

R: <\/strong>Bir sistemin sadece birka\u00e7 olas\u0131 i\u00e7 durumu ve tamamen basit kurallarla idare edilen davran\u0131\u015flar\u0131 olsa bile, davran\u0131\u015flar\u0131na y\u00f6nelik a\u00e7\u0131klamalar \u00fcretebilmek izlenemez olmaya devam eder. Sizce insan bili\u015fi bundan daha m\u0131 basittir?<\/p>\n\n\n\n

C: <\/strong>Hay\u0131r, muhtemelen daha karma\u015f\u0131kt\u0131r.<\/p>\n\n\n\n

R: <\/strong>O zaman bizim izlenemezlik sonu\u00e7lar\u0131m\u0131z sizin \u00e7al\u0131\u015fmalar\u0131n\u0131za uyarlanabilir.<\/p>\n\n\n\n

C: <\/strong>\u00c7al\u0131\u015fmam\u0131n umutsuz oldu\u011funu mu s\u00f6yl\u00fcyorsunuz? Ben hi\u00e7 bili\u015f i\u00e7in tatmin edici bir a\u00e7\u0131klama getirmeyi umamayacak m\u0131y\u0131m?<\/p>\n\n\n\n

R: <\/strong>Umutsuz demeyelim. \u015eans eseri tatmin edici bir a\u00e7\u0131klama bulabilirseniz, o zaman bunun fark\u0131na var\u0131rs\u0131n\u0131z.<\/p>\n\n\n\n

C: <\/strong>(i\u00e7 \u00e7eki\u015f) Bu pek de bir plana benzemiyor.<\/p>\n\n\n\n

R: <\/strong>Bence izlenemezlik konusu, h\u00e2lihaz\u0131rda u\u011fra\u015ft\u0131\u011f\u0131n\u0131zdan, verinin, genellemelerinin ve teorinin \u00f6z\u00fcndeki belirsizlikten daha fazla cesaretinizi k\u0131rmamal\u0131. Yine de bu durum, \u00e7\u0131kar\u0131m \u00e7al\u0131\u015fmalar\u0131n\u0131z\u0131n etkili bir \u015fekilde s\u00fcre\u00e7 haline getirilemeyece\u011fini g\u00f6steriyor. Dolay\u0131s\u0131yla bir algoritma olu\u015fturmaya \u00e7al\u0131\u015fmay\u0131n ya da bilimsel d\u00fc\u015f\u00fcncenizin yerini alacak, s\u0131k\u0131 kurallar dizisi olu\u015fturmay\u0131n.<\/p>\n\n\n\n

C:<\/strong> Neden olmas\u0131n? Bu, neden yanl\u0131\u015f olur?<\/p>\n\n\n\n

R: <\/strong>Ger\u00e7ekte d\u00fc\u015f\u00fcnd\u00fcklerinizin d\u0131\u015f\u0131nda kalan astronomik b\u00fcy\u00fckl\u00fckte bir alan\u0131n k\u00fc\u00e7\u00fck bir k\u0131sm\u0131nda s\u0131k\u0131\u015fm\u0131\u015fken, kendinizi t\u00fcm alan\u0131 ara\u015ft\u0131rd\u0131\u011f\u0131n\u0131z d\u00fc\u015f\u00fcncesiyle kand\u0131r\u0131yor olabilirsiniz. Ayn\u0131 zamanda bu, \u00e7al\u0131\u015ft\u0131\u011f\u0131n\u0131z sistemin ger\u00e7ekten inand\u0131\u011f\u0131n\u0131zdan daha basit oldu\u011funu d\u00fc\u015f\u00fcnmenize yol a\u00e7abilir, \u00e7\u00fcnk\u00fc aksi halde s\u00fcre\u00e7leriniz etkili bir bi\u00e7imde ayn\u0131 noktada bulu\u015fmaz (converge<\/em>).<\/p>\n\n\n\n

C:<\/strong> Peki kullanabilece\u011fim herhangi bir s\u00fcre\u00e7 ilerlememi engelleyebilecekse, bu durumda ben ne yapabilirim?<\/p>\n\n\n\n

R: <\/strong>Ben s\u00fcre\u00e7le\u015ftirmenin kar\u015f\u0131s\u0131nda bir meta-yakla\u015f\u0131m \u00f6neririm. Bu, bili\u015fsel bilimde giderek daha dar metodolojik yakla\u015f\u0131m setlerine odakland\u0131\u011f\u0131m\u0131z \u015fu anda, daha da \u00f6nemlidir. Verebilece\u011fim en iyi tavsiye toplulu\u011fa ili\u015fkindir: Zihni anlamak i\u00e7in tek umudumuz, bu toplulu\u011fun yakla\u015f\u0131mlarda ve farkl\u0131 ara\u015ft\u0131rmac\u0131lar\u0131n benimseyebilece\u011fi s\u0131n\u0131rs\u0131z say\u0131da s\u00fcre\u00e7te \u00e7o\u011fulculu\u011fa olanak sa\u011flamas\u0131d\u0131r.<\/p>\n\n\n\n

C:<\/strong> Neden s\u0131n\u0131rs\u0131z?<\/p>\n\n\n\n

R: <\/strong>\u00c7\u00fcnk\u00fc izlenemez problemlerin belirli<\/em> say\u0131da paralel s\u00fcre\u00e7le \u00e7\u00f6z\u00fclemedi\u011fi biliniyor.<\/p>\n\n\n\n

C:<\/strong> Ama yakla\u015f\u0131mlar\u0131n say\u0131s\u0131na bir s\u0131n\u0131r koymazsak, ayn\u0131 zamanda bir\u00e7ok k\u00f6t\u00fc yakla\u015f\u0131m olmaz m\u0131?<\/p>\n\n\n\n

R: <\/strong>Alternatif yakla\u015f\u0131mlara ihtiya\u00e7 oldu\u011funu ve bunlar\u0131n ge\u00e7erliliklerini kabul etmek, yap\u0131c\u0131 ele\u015ftirinin \u00f6nko\u015fuludur. Yani, yakla\u015f\u0131mlar\u0131 sa\u011flam temellere dayand\u0131rarak ele\u015ftirebilirsiniz, ama sizi herhangi bir sabit s\u00fcreci (leri\/ setlerini) do\u011fru olarak atfedip, di\u011ferlerini de bunu benimsemeye ikna etmeye \u00e7al\u0131\u015fmaktan vazge\u00e7irmeliyim. Baz\u0131 meslekta\u015flar\u0131n\u0131z\u0131n kulland\u0131\u011f\u0131 fazla \u00f6znel metotlardan \u015fik\u00e2yet etti\u011finizi fark ettim; ya\u015famal\u0131 ve size ayk\u0131r\u0131 gelen bu fikirleri ya\u015fatmal\u0131s\u0131n\u0131z.<\/p>\n\n\n\n

Te\u015fekk\u00fcr<\/strong><\/h2>\n\n\n\n

Yazarlar, metnin \u00f6nceki versiyonuna yapm\u0131\u015f olduklar\u0131 faydal\u0131 yorumlar i\u00e7in anonim inceleyicilere ve bu ara\u015ft\u0131rmaya ilham olan tart\u0131\u015fmalar\u0131 i\u00e7in Berna Devezer\u2019a te\u015fekk\u00fcrlerini sunar. TW, NSERC Discovery Grant 228104\u20132015 taraf\u0131ndan desteklenmi\u015ftir. IvR; Schloss Dagstuhl\u2019a: geri \u00e7ekilmi\u015f ara\u015ft\u0131rmaya (nr. 19299) desteklerinden dolay\u0131 Leibniz Enformatik Merkezi\u2019ne ve Netherlands Institute for Advanced Studies in the Humanities and Social Sciences (NIAS-KNAW)\u2019a ve 2020\/21 Distinguished Lorentz Fellowship \u00f6d\u00fcl\u00fc i\u00e7in Lorentz Center\u2019a te\u015fekk\u00fcrlerini sunar.<\/p>\n\n\n\n

KAYNAK\u00c7A<\/strong><\/h1>\n\n\n\n

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[63] O\u2019Connor, C., & Bruner, J. (2019). Dynamics and diversity in epistemic communities. Erkenntnis, 84<\/em>(1), 101\u2013119.<\/p>\n","protected":false},"featured_media":2010,"template":"","meta":{"_acf_changed":false},"event_publishing_tags":[98,94,93,262,691,64,92,323,283,997,74,999,1001,998,284,475,75,261,351,726,474,473,1000],"kategori":[305],"class_list":["post-2009","blog_content","type-blog_content","status-publish","has-post-thumbnail","hentry","event_publishing_tags-bilim-felsefesi","event_publishing_tags-bilis","event_publishing_tags-bilissel-bilim","event_publishing_tags-bilissel-bilim-felsefesi","event_publishing_tags-cogist","event_publishing_tags-cognition","event_publishing_tags-cognitive-science","event_publishing_tags-cogsci","event_publishing_tags-complexity","event_publishing_tags-computational-complexity","event_publishing_tags-felsefe","event_publishing_tags-hesaplamali-karmasiklik","event_publishing_tags-intractability","event_publishing_tags-islemlemesel-karmasiklik","event_publishing_tags-karmasiklik","event_publishing_tags-kuram","event_publishing_tags-philosophy","event_publishing_tags-philosophy-of-cognitive-science","event_publishing_tags-philosophy-of-science","event_publishing_tags-philsci","event_publishing_tags-teori","event_publishing_tags-theory","event_publishing_tags-tractable-cognition","kategori-ceviri"],"acf":[],"_links":{"self":[{"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/blog_content\/2009","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/blog_content"}],"about":[{"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/types\/blog_content"}],"version-history":[{"count":0,"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/blog_content\/2009\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/media\/2010"}],"wp:attachment":[{"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/media?parent=2009"}],"wp:term":[{"taxonomy":"event_publishing_tags","embeddable":true,"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/event_publishing_tags?post=2009"},{"taxonomy":"kategori","embeddable":true,"href":"https:\/\/cog-ist.com\/en\/wp-json\/wp\/v2\/kategori?post=2009"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}