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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Book ChapterDOI
Encoding Solutions of the Frame Problem in Dynamic Logic
TL;DR: The results of the paper show that dynamic logic, as one of the formalisms for reasoning about dynamic domains, can be used as a formal tool for comparing and unifying logics of action.
Journal ArticleDOI
An ontological framework for web service processes
Claus Pahl,Ronan Barrett +1 more
TL;DR: This work proposes a framework for the compositional definition of Web services based on the π-calculus to define protocol-like restrictions on service interactions and based on description logic and ontologies to guide the discovery and modelling of services and processes.
Book ChapterDOI
Composing Partially Ordered Monads
Patrik Eklund,Robert Helgesson +1 more
TL;DR: Composition of the many-valued powerset partially ordered monad with the term monad provides extensions to non-classical relations and also new examples for Kleene algebras.
Journal ArticleDOI
Non-terminating processes in the situation calculus
TL;DR: This paper describes a situation calculus approach to expressing and proving properties of non-terminating programs expressed in Golog, a high level logic programming language for modeling and implementing dynamical systems.
Game Constructions that are Safe for Bisimulation
TL;DR: It is shown that all game constructions of GL are safe for bisimulation, i.e. that an atomic bisimulations can be lifted to non-atomic games constructed by the operations of GL.
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.