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Logics of Programs.

Dexter Kozen, +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.

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Citations
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The Denotational Semantics Definition of PLC Programs Based on Extended λ -Calculus

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Abstract Model Checking with SOFL Hierarchy

TL;DR: This paper presents a new abstract model checking approach for efficient verification of software in large scale by utilizing SOFL hierarchy, and within this approach, programs are verified from the high-level to low-level structures, and the state space throughout the verification can be effectively controlled.
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A Probabilistic Model Checking Approach to Investigate the Palytoxin Effects on the Na + /K + -ATPase

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Interference Analysis for Dependable Systems Using Refinement and Abstraction

TL;DR: A two-layered modal specification notation will allow the specification of services and protocols for distributed dependable systems and their properties and will play the key roles in an integrated development and analysis framework.
References
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Proceedings ArticleDOI

The temporal logic of programs

Amir Pnueli
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.