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Open AccessProceedings ArticleDOI

Intuitionistic linear logic and partial correctness

Dexter Kozen, +1 more
- pp 259-268
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TLDR
A Gentzen-style sequent calculus for partial correctness that subsumes propositional Hoare logic and is a noncommutative intuitionistic linear logic that proves soundness and completeness over relational and trace models.
Abstract
We formulate a Gentzen-style sequent calculus for partial correctness that subsumes propositional Hoare logic. The system is a noncommutative intuitionistic linear logic. We prove soundness and completeness over relational and trace models. As a corollary, we obtain a complete sequent calculus for the inclusion and equivalence of regular expressions.

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Citations
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Journal ArticleDOI

Automata on Guarded Strings and Applications

TL;DR: It is shown that a basic result of the theory of Boolean decision diagrams (BDDs), namely that minimal ordered BDDs are unique, is a special case of the Myhill-Nerode theorem for a class of automata on guarded strings.

Kleene Algebra with Tests and Program Schematology

TL;DR: A purely algebraic approach to scheme equivalence using Kleene algebra with tests (KAT), where instead of transforming schemes directly using combinatorial graph manipulation, they are regarded as a certain kind of automaton on abstract traces.

On the Elimination of Hypotheses in Kleene Algebra with Tests

TL;DR: In this paper, it was shown how to eliminate hypotheses of the form cp = c for atomic p. This reduction is known as elimination of hypotheses and is useful in eliminating redundant code and arise quite often in the verification of compiler optimizations.
Journal ArticleDOI

Some results in dynamic model theory

TL;DR: This work exhibits a Kripke frame U whose trace algebra TrU is universal for the equational theory of Tarskian trace algebras over Σ satisfying T, although U itself is not TarsKian in general.

Properties of Invariants and Induction Lemmata

TL;DR: It is proved that the set of induction lemmata to be used in Park's fixpoint induction rule for greatest fixpoints is closed both under conjunction and disjunction, and therefore, this set is a lattice and there is a weakest and a strongest induction lemma.
References
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Journal ArticleDOI

Linear logic

Journal ArticleDOI

Linear logic

Patrick Lincoln
- 01 May 1992 - 
TL;DR: This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.
Book

Proofs and types

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.
Book

Dynamic Logic

TL;DR: This book provides the first comprehensive introduction to Dynamic Logic, a system of remarkable unity that is theoretically rich as well as of practical value.
Journal ArticleDOI

Propositional dynamic logic of regular programs

TL;DR: A formal syntax and semantics for the propositional dynamic logic of regular programs is defined and principal conclusions are that deciding satisfiability of length n formulas requires time d n /log n for some d > 1, and that satisfiability can be decided in nondeterministic time cn for some c.
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