In this paper we present a logic for dealing with preorders, where functions and predicates behave monotonically or antimonotonically in their arguments, and incorporating order-sorted relations into the syntax of the language. For this logic a ground tableau-based deduction method and a free variable extension version are proposed, proving their soundness and completeness. Finally, an implemen...

We present a calculus that integrates equality handling by superposition into a free variable tableau calculus. We prove completeness of this calculus by an adaptation of the model generation [1, 15] technique commonly used for completeness proofs of resolution calculi. The calculi and the completeness proof are compared to earlier results of Degtyarev and Voronkov [7].

We present algorithms for uniication and anti-uniication in the Calculus of Constructions, where occurrences of free variables (the variables subject to in-stantiation) are restricted to higher-order patterns, a notion investigated for the simply-typed-calculus by Miller. Most general uniiers and least common anti-instances are shown to exist and are unique up to a simple equivalence. The uniic...

Cats are nice. (: : :) because cats never overlap. Abstract In this paper we discuss two approaches to adverbial quantiication, the so-called`bound variable approach' and thèsituation-based approach', and we address the suggestion that has been made in the literature that the latter reduces to the former as soon as the underlying structure of situations has been characterized at the required le...

We discuss an adaptation of the technique of saturation up to redundancy, as introduced by Bachmair and Ganzinger [1], to tableau and sequent calculi for classical first-order logic. This technique can be used to easily show the completeness of optimized calculi that contain destructive rules e.g. for simplification, rewriting with equalities, etc., which is not easily done with a standard Hint...

Human beings seem to be resilient and have a great capacity to overcome adverse circumstances. One apparent variable that may predict people’s emotional and physical health after a trauma is their general level of psychological well-being (McMillen, Smith, & Fisher, 1997). The current study explores the role of subjective vitality and the perception of stress as mediators between general life s...

For conditional probabilistic knowledge bases with conditionals based on propositional logic, the principle of maximum entropy (ME) is well-established, determining a unique model inductively completing the explicitly given knowledge. On the other hand, there is no general agreement on how to extend the ME principle to relational conditionals containing free variables. In this paper, we focus o...

The aim of this work is to show how hypergraphs can be used as a systematic tool in the classi!cation of continuous boolean functions according to their degree of parallelism. Intuitively f is “less parallel” than g if it can be de!ned by a sequential program using g as its only free variable. It turns out that the poset induced by this preorder is (as for the degrees of recursion) a sup-semila...

In this paper several conceptual extensions to the theory of order-restricted free variable clausal tableaux which was initiated in 9, 8] are presented: atom orderings are replaced by the more general concept of a selection function, the substitutivity condition required for lifting is for certain variants of the calculus replaced by a much weaker assumption, and a rst version of order-restrict...

The equations that define the Lax pairs for generalized principal chiral models can be solved for any constant nondegenerate bilinear form on su(2). The solution is dependent on one free variable that can serve as the spectral parameter. Necessary conditions for the nonconstant metric on SU(2) that define the integrable models are given. 1991 MSC numbers: 35L10, 35L15, 34A55