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Linear logic

About: Linear logic is a research topic. Over the lifetime, 2439 publications have been published within this topic receiving 56348 citations.


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Journal ArticleDOI
30 Jan 1987

3,947 citations

Book ChapterDOI
29 Mar 2004
TL;DR: This work introduces a temporal logic of calls and returns (CaRet) for specification and algorithmic verification of correctness requirements of structured programs and presents a tableau construction that reduces the model checking problem to the emptiness problem for a Buchi pushdown system.
Abstract: Model checking of linear temporal logic (LTL) specifications with respect to pushdown systems has been shown to be a useful tool for analysis of programs with potentially recursive procedures. LTL, however, can specify only regular properties, and properties such as correctness of procedures with respect to pre and post conditions, that require matching of calls and returns, are not regular. We introduce a temporal logic of calls and returns (CaRet) for specification and algorithmic verification of correctness requirements of structured programs. The formulas of CaRet are interpreted over sequences of propositional valuations tagged with special symbols call and ret. Besides the standard global temporal modalities, CaRet admits the abstract-next operator that allows a path to jump from a call to the matching return. This operator can be used to specify a variety of non-regular properties such as partial and total correctness of program blocks with respect to pre and post conditions. The abstract versions of the other temporal modalities can be used to specify regular properties of local paths within a procedure that skip over calls to other procedures. CaRet also admits the caller modality that jumps to the most recent pending call, and such caller modalities allow specification of a variety of security properties that involve inspection of the call-stack. Even though verifying context-free properties of pushdown systems is undecidable, we show that model checking CaRet formulas against a pushdown model is decidable. We present a tableau construction that reduces our model checking problem to the emptiness problem for a Buchi pushdown system. The complexity of model checking CaRet formulas is the same as that of checking LTL formulas, namely, polynomial in the model and singly exponential in the size of the specification.

3,516 citations

Book
01 Jan 1989
TL;DR: In this paper, the Curry-Howard isomorphism and the normalisation theorem of a natural deduction system T coherence spaces have been studied in the context of linear logic and linear logic semantics.
Abstract: Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system F coherence semantics of the sum cut elimination (Hauptsatz) strong normalisation for F representation theorem semantics of System F what is linear logic?

1,771 citations

Journal ArticleDOI
TL;DR: A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language.

687 citations

Journal ArticleDOI
TL;DR: A logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side is introduced and computational interpretations, based on sharing, at both the propositional and predicate levels are discussed.
Abstract: We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers and which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels.

522 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202315
202231
202155
202078
2019101
2018104