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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
Citations
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Reasoning about High-Level Robot Behaviors by Model Checking and Local Validity Tests
TL;DR: A logical formalism that combines a very expressive logic of programs, the modal mu-calculus, with a special use of a minimal knowledge operator is introduced, which allows for exploiting existing model checking techniques and systems for reasoning about complex highlevel robot behaviors.
Book ChapterDOI
Interval Approach to Parallel Timed Systems Verification
Yuri Karpov,Dmitry Sotnikov +1 more
TL;DR: The interval approach to hybrid system verification is presented and it is demonstrated that the approach is natural for parallel timed systems, use it for temporal logic verification and parameter analysis.
Proceedings Article
Infinitary Queries and Their Asymptotic Probabilities I: Properties Definable in Transitive Closue Logic
TL;DR: In this article, a general method for proving that the limit law fails for certain classes of finite structures expressible in transitive closure logic is presented, and all associated asymptotic problems are undecidable.
Journal ArticleDOI
Canonical finite models of Kleene algebra with tests
TL;DR: Applications of an effective procedure of constructing from each KAT term p a finite KAT model K ( p ) that will be called the canonical finite model of the KATterm p .
Book ChapterDOI
Rabin Tree Automata and Finite Monoids
TL;DR: Strong monoid recognizability of infinite tree languages is introduced and it is shown that there exists an infinite tree language L which is not Rabin recognizable, but its associated language L is monoid recognizable (in the standard sense).
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.