Open Access
Logics of Programs.
Dexter Kozen,Jerzy Tiuryn +1 more
- pp 789-840
TLDR
In this paper, the authors present an introduction to some of the basic issues in the study of program logics and discuss their syntax, semantics, proof theory, and expressiveness.Abstract:
Publisher Summary This chapter presents an introduction to some of the basic issues in the study of program logics. The chapter describes various forms of first-order Dynamic Logic and discusses their syntax, semantics, proof theory, and expressiveness. The chapter discusses the power of auxiliary data structures such as arrays and stacks, and a powerful assignment statement called the nondeterministic assignment. Program logics differ from classical logics in that truth is dynamic rather than static. In classical predicate logic, the truth value of a formula is determined by a valuation of its free variables over some structure. The valuation and the truth value of the formula it induces are regarded as immutable. In program logics, there are explicit syntactic constructs called programs to change the values of variables, thereby changing the truth values of formulas. There are two main approaches to modal logics of programs: (1) the exogenous approach, exemplified by Dynamic Logic and its precursor, the Partial Correctness Assertions Method; and (2) the endogenous approach, exemplified by Temporal Logic and its precursor, the Inductive Assertions Method.read more
Citations
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Intuitionistic LTL and a New Characterization of Safety and Liveness
TL;DR: It is demonstrated that ILTL is suitable for assume-guarantee reasoning and for expressing properties that relate finite and infinite behaviors, and admits an elegant logical characterization of safety and liveness properties.
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Monad-independent Dynamic Logic in HasCasl
Lutz Schröder,Till Mossakowski +1 more
TL;DR: This work extends the Hoare calculus for partial correctness of monadic programs to a monad-independent dynamic logic, and uses the logic of HASCASL, a higher-order language for functional specification and programming.
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A hybrid algorithm for LTL games
TL;DR: This work presents a practical hybrid algorithm--a combination of symbolic and explicit algorithm--for the computation of winning strategies for unrestricted LTL games that has been successfully applied to synthesize reactive systems with up to 1011 states.
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Description Logics with Inverse Roles, Functional Restrictions, and N-ary Relations
TL;DR: This paper exploits the correspondence between DLs and propositional dynamic logics as a framework to investigate the decidability and the complexity of a powerful DL, and shows that such DL is suitable to represent n-ary relations, as needed in the applications of class-based formalisms to databases.
References
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Proceedings ArticleDOI
The temporal logic of programs
TL;DR: A unified approach to program verification is suggested, which applies to both sequential and parallel programs, and the main proof method is that of temporal reasoning in which the time dependence of events is the basic concept.
Book ChapterDOI
Temporal and modal logic
TL;DR: In this article, a multiaxis classification of temporal and modal logic is presented, and the formal syntax and semantics for two representative systems of propositional branching-time temporal logics are described.
Journal ArticleDOI
An axiomatic basis for computer programming
TL;DR: An attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics.
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.