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Logics of Programs.
Dexter Kozen,Jerzy Tiuryn +1 more
- pp 789-840
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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
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Metalogic, Qualia, and Identity on Neptune’s Great Moon: Meaning and Mathematics in the Works of Joseph A. Goguen and Samuel R. Delany
TL;DR: This essay attempts to draw out some of the parallels between the works of Joseph A. Goguen and Samuel R. Delany, in particular regarding metalogic, qualia, and identity, using illustrative examples from theWorks of both authors.
Lazy-formalization to the Frame Problem
Norman Foo,Dongmo Zhang +1 more
TL;DR: It is shown that the frame axioms which are required for answering a query involve only the objects which are relevant to the query and action description, and the frame problem may be mitigated by localizing descriptions and avoiding the listing of frameAxioms.
Journal ArticleDOI
Separation of Test-Free Propositional Dynamic Logics over Context-Free Languages
TL;DR: For regular, visibly pushdown and deterministic context-free languages, the separation of the respective PDLs can be proven by automata-theoretic techniques as mentioned in this paper.
Book ChapterDOI
Correctness of Rule Programs
TL;DR: This chapter studying the semantics of rule programs from the viewpoint of the relation between their initial and final states defines correctness formulas in the classical form of so-called Hoare triples, where r is a rule.
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.