Introduction to Cirquent Calculus and Abstract Resource Semantics
نویسندگان
چکیده
منابع مشابه
Introduction to Cirquent Calculus and Abstract Resource Semantics
This paper introduces a refinement of the sequent calculus approach called cirquent calculus. Roughly speaking, the difference between the two is that, while in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint and independent sequences of formulas, in cirquent calculus they are permitted to share elements. Explicitly allowing or disallowing shared resources and thus tak...
متن کاملCirquent calculus deepened
Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuit-style structures (called cirquents), as opposed to the more traditional approaches that deal with tree-like objects such as formulas, sequents or hypersequents. Among its advantages are greater efficiency, flexibility and expressiveness. This paper presents a detailed e...
متن کاملSoundness and completeness of the cirquent calculus system CL6 for computability logic
Computability logic is a formal theory of computability. The earlier article “Introduction to cirquent calculus and abstract resource semantics” by Japaridze proved soundness and completeness for the basic fragment CL5 of computability logic. The present article extends that result to the more expressive cirquent calculus system CL6, which is a conservative extension of both CL5 and classical p...
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We show that the uniform validity is equivalent to the non-uniform validity for Blass’ semantics of [A game semantics for linear logic. Annals of Pure and Applied Logic 56 (1992) 183–220]. We present a shorter proof (than that of [G. Japaridze. The intuitionistic fragment of computability logic at the propositional level. Annals of Pure and Applied Logic 147 (2007), No.3, pp.187-227]) of the co...
متن کاملDeduction Theorem for Symmetric Cirquent Calculus
Cirquent calculus is a recent approach to proof theory, whose characteristic feature is being based on circuit-style structures (called cirquents) instead of the traditional formulas or sequents. In this paper we prove the deduction theorem for the symmetric version of cirquent calculus, and show that the derivation in the deduction theorem will be at most polynomially longer than the proof of ...
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ژورنال
عنوان ژورنال: Journal of Logic and Computation
سال: 2006
ISSN: 0955-792X,1465-363X
DOI: 10.1093/logcom/exl005