The first-order hypothetical logic of proofs
نویسندگان
چکیده
منابع مشابه
Hypothetical Logic of Proofs
The Logic of Proofs (LP) [2–5] is a refinement of modal logic introduced by Artemov in 1995 which has recently been proposed for explaining well-known paradoxes arising in the formalization of Epistemic Logic. Assertions of knowledge and belief are accompanied by justifications: the formula [[t]]A states that proof witness t is “reason” for knowing/believing A. Also, LP is capable of reflecting...
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We study a term assignment for an intuitonistic fragment of the Logic of Proofs (LP). LP is a refinement of modal logic S4 in which the assertion 2A is replaced by [[s]]A whose intended reading is “s is a proof of A”. We first introduce a natural deduction presentation based on hypothetical judgements and then its term assignment, which yields a confluent and strongly normalising typed lambda c...
متن کاملOn First Order Logic of Proofs
The Logic of Proofs LP solved long standing Gödel’s problem concerning his provability calculus (cf. [4]). It also opened new lines of research in proof theory, modal logic, typed programming languages, knowledge representation, etc. The propositional logic of proofs is decidable and admits a complete axiomatization. In this paper we show that the first order logic of proofs is not recursively ...
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1 ) I t i s the most t r a d i t i o n a l , i . e . luetanuith ema t i cs , as i t appears in l o g i c books, i s u s u a l l y s t a t e d i n terms o f s t r i n g s . 2) Axioms in terras of a b s t r a c t syn tax are s imply theorems o f the theory expressed in terms of s t r i n g s . Thus the two r e p r e s e n t a t i o n s look sub s t a n t i a l l y the same w i t h respec t t o " ...
متن کاملCyclic Proofs for First-Order Logic with Inductive Definitions
We consider a cyclic approach to inductive reasoning in the setting of first-order logic with inductive definitions. We present a proof system for this language in which proofs are represented as finite, locally sound derivation trees with a “repeat function” identifying cyclic proof sections. Soundness is guaranteed by a well-foundedness condition formulated globally in terms of traces over th...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2016
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exv090