Author
Evert W. Beth
Bio: Evert W. Beth is an academic researcher from University of Amsterdam. The author has contributed to research in topics: Philosophy of science & Philosophy of language. The author has an hindex of 11, co-authored 51 publications receiving 1028 citations.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the authors discuss a situation which is known from classical mechanics: the state of a certain material system at an epoch t is characterized by the values of the canonical variables q and p, the number of which may be reduced, for the sake of brevity and simplicity, to one of each type.
Abstract: (1) In order to characterize the kind of problem which I wish to consider, I first briefly discuss a situation which is known from classical mechanics. The state of a certain material system at an epoch t is characterized by the values of the canonical variables q and p, the number of which may be reduced, for the sake of brevity and simplicity, to one of each type.
51 citations
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01 Jun 1962
31 citations
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TL;DR: In this article, a semantical analysis of modal logic ii and non-normal modal propositional calculi is presented, and the tableaux that leads to a decision procedure for the propositional calculus is considered.
Abstract: Publisher Summary This chapter discusses semantical analysis of modal logic ii and non-normal modal propositional calculi. The proof of sufficiency, which is omitted by many, proceeds by constructing a normal characteristic matrix by Lindenbaum's method. The tableaux that leads to a decision procedure for the propositional calculi is considered.
1,174 citations
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01 Jan 1979
TL;DR: This paper presents a meta-modelling simulation of the response of the immune system to changes in the environment through the course of natural selection.
Abstract: • Constraint domains in which the possible values that a variable can take are restricted to a finite set. • Examples: Boolean constraints, or integer constraints in which each variable is constrained to lie in within a finite range of integers. • Widely used in constraint programming. • Many real problems can be easily represented using constraint domains, e.g.: scheduling, routing and timetabling. • They involve choosing amongst a finite number of possibilities. • Commercial importance to many businesses: e.g. deciding how air crews should be allocated to aircraft flights. • Developed methods by different research communities: Arc and node consistency techniques (artificial intelligence). Bounds propagation techniques (constraint programming). Integer programming (operations research).
1,123 citations
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31 Jul 2012TL;DR: This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style and is intended for those interested in computer science and mathematics at the beginning graduate level.
Abstract: This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style. Applications to automated theorem proving are considered and usable programs in Prolog are provided. This material can be used both as a first text in formal logic and as an introduction to automation issues, and is intended for those interested in computer science and mathematics at the beginning graduate level. The book begins with propositional logic, then treats first-order logic, and finally, first-order logic with equality. In each case the initial presentation is semantic: Boolean valuations for propositional logic, models for first-order logic, and normal models when equality is added. This defines the intended subjects independently of a particular choice of proof mechanism. Then many kinds of proof procedures are introduced: tableau, resolution, natural deduction, Gentzen sequent and axiom systems. Completeness issues are centered in a model existence theorem, which permits the coverage of a variety of proof procedures without repetition of detail. In addition, results such as compactness, interpolation, and the Beth definability theorem are easily established. Implementations of tableau theorem provers are given in Prolog, and resolution is left as a project for the student.
1,099 citations
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TL;DR: A model and proof theories, a proof procedure, and applications for one non-monotonic logic are developed, and it is proved the completeness of the non-Monotonic predicate calculus and the decidability of theNon- monotonic sentential calculus.
982 citations
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TL;DR: The present paper attempts to state and prove a completeness theorem for the system S5 of [1], supplemented by first-order quantifiers and the sign of equality.
Abstract: The present paper attempts to state and prove a completeness theorem for the system S5 of [1], supplemented by first-order quantifiers and the sign of equality. We assume that we possess a denumerably infinite list of individual variables a, b, c, …, x, y, z, …, xm, ym, zm, … as well as a denumerably infinite list of n-adic predicate variables Pn, Qn, Rn, …, Pmn, Qmn, Rmn,…; if n=0, an n-adic predicate variable is often called a “propositional variable.” A formula Pn(x1, …,xn) is an n-adic prime formula; often the superscript will be omitted if such an omission does not sacrifice clarity.
851 citations