Type Theory and its Meaning Explanations
نویسنده
چکیده
At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations”; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort arise naturally as enrichments of logical theories with further judgements, and contrast this with modern proof-theoretic type theories which interpret the judgements and proofs of logics, not their propositions and verifications.
منابع مشابه
Meaning explanations at higher dimension
Martin-Löf’s intuitionistic type theory is a widely-used framework for constructive mathematics and computer programming. In its most popular form, type theory consists of a collection of inference rules inductively defining formal proofs. These rules are justified by Martin-Löf’s meaning explanations, which extend the Brouwer-Heyting-Kolmogorov interpretation of connectives to a rich collectio...
متن کاملProgram Testing and the Meaning Explanations of Intuitionistic Type Theory
The relationship between program testing and Martin-Löf’s meaning explanations for intuitionistic type theory is investigated. The judgements of intuitionistic type theory are viewed as conjectures which can be tested in order to be corroborated or refuted. This point of view provides a new perspective on the meaning of hypothetical judgements, since tests for such judgements need methods for g...
متن کاملInvestigating “Accord Theory” of Abdulghaher Jorjani and Jacques Augustin Berque in Eliminating Inconsistencies in the Apparent Meaning of the Quran (Case-study of the Sura of Ahqaf)
Abstract In recent era, debates around the inconsistency in the apparent meaning of Suras and Verses of the Quran has been abundant among the contemporary Quran researchers. On the other hand, many Islamic scientists and non-Islamic researchers have striven to prove the consistency of the apparent meaning of the Verses of the Quran and have put forward theories from which we may mention the “th...
متن کاملInvestigating “Accord Theory” of Abdulghaher Jorjani and Jacques Augustin Berque in Eliminating Inconsistencies in the Apparent Meaning of the Quran (Case-study of the Sura of Ahqaf)
Abstract In recent era, debates around the inconsistency in the apparent meaning of Suras and Verses of the Quran has been abundant among the contemporary Quran researchers. On the other hand, many Islamic scientists and non-Islamic researchers have striven to prove the consistency of the apparent meaning of the Verses of the Quran and have put forward theories from which we may mention the “th...
متن کاملAttributions as Behavior Explanations: Toward a New Theory
Attribution theory has played a major role in social-psychological research. Unfortunately, the term attribution is ambiguous. According to one meaning, forming an attribution is making a dispositional (trait) inference from behavior; according to another meaning, forming an attribution is giving an explanation (especially of behavior). The focus of this paper is on the latter phenomenon of beh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1512.01837 شماره
صفحات -
تاریخ انتشار 2015