R. Jim Cunningham

A Prolog implementation of a new theorem-prover for first-order classical logic is described. The prover is based on the calculus KE and the rules used for analysing quantifiers in free variable semantic tableaux. A formal specification of the rules used in the implementation is described, for which soundness and completeness is straightforwardly verified. The prover has been tested on the first 47 problems of the Pelletier set, and its performance compared with a state of the art semantic tableaux theorem-prover. It has also been applied to model building in a prototype system for logical animation, a technique for symbolic execution which can be used for validation. The interest of these experiments is that they demonstrate the value of certain “characteristics” of the KE calculus, such as the significant space-saving in theorem-proving, the mutual inconsistency of open branches in KE trees, and the relation of the KE rules to “traditional” forms of reasoning

Linguistic phenomena of tense and aspect have been investigated in a great deal of theoretical work in linguistics, philosophy and computer science. Modern tense logics, established by Prior, are part of this effort. Point tense logics offer an intuitive representation of tense but lack the expressiveness to represent many aspectual structures. Interval tense logics offer more expressiveness but in the general case can be computationally intractable. From a linguistic perspective there is the problem of precisely how to formalise the aspectual structures, such as a culmination and a culminated process. In this paper we define a computationally tractable augmented fragment of Halpern and Shoham's interval tense logic HS and apply it to represent a core set of aspectual structures, which are incorporated into a temporal semantics of a simple fragment of English. We model the logic fragment using timelines and define two procedures, one for constructing the minimal timelines that satisfy a formula and one for checking semantic entailments between one formula and another by comparing their timelines. The former is applied to compute models of temporal readings and the latter to check entailments between them. Possible extensions to the logic fragment and timeline models are discussed as ways of accounting for a wider range of linguistic behaviour.