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
A Temporal Logic of Nested Calls and Returns
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.
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.
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.
Book ChapterDOI
Automata on infinite objects
TL;DR: This chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree.
Book ChapterDOI
Languages, automata, and logic
TL;DR: The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.
References
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Book ChapterDOI
On the Duality of Dynamic Algebras and Kripke Models
TL;DR: A natural topology is introduced on Kripke models of propositional dynamic logic (PDL) and a useful duality is exhibited analogous to the duality between Boolean algebras and their Stone spaces.
Proceedings ArticleDOI
On the theory of programming logics
TL;DR: This paper proves the completeness and decidability of the monadic (iterative) programming logic, and discusses the polyadic logic and the programming language briefly, and considers general models for the iterative programming logic.
Book ChapterDOI
Propositional Dynamic Logics of Programs: a Survey
TL;DR: Dynamic algebras were introduced in [K1] and have been studied by Pratt, Reiterman and Trnkova, Nemeti, and the author [Kl-5] and a survey of these results follows.
Journal ArticleDOI
A programming language for the inductive sets, and applications
David Harel,Dexter Kozen +1 more
TL;DR: A programming language IND that generalizes alternating Turing machines to arbitrary first-order structures and provides a natural query language for the set of fixpoint queries over a relational database is introduced.