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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...

In this paper we describe how a combination of the classical “universal” E-unification and “rigid” Eunification, called “mixed” E-unification, can be used to efficiently handle equality in universal formula semantic tableaux, that are an extension of free variable tableaux.

Van Lambalgen (1990) proposed a translation from a language containing a generalized quantifier Q into a first-order language enriched with a family of predicates Rs, for every arity i (or an infinitary predicate R) which takes Qz~(z, yl, . . . , y,~) to Vz(R(z, yl,..., g,~) --" ~b(x, Yl,..., Y,~)) (gl . . . . . g~ are precisely the free variables of Qzq~). The logic of Q (without ordinary quan...

We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain \free" and \universal" variables. Our \lean" Prolog implementation is not only surprisingly short, but compares favourably with other considerably more complex implementations for modal deduction.

In this paper, we present a further liberalization of the-rule in free variable semantic tableaux. It is eeective in that (1) it is both a natural and intuitive liberalization, and (2) can reduce the proof size non elementarily as compared to previous versions of the-rule.

We apply the framework of the generic δ-rule presented in [4] to show how to map the δ-rule, which uses ǫ-terms as syntactical objects to expand existentially quantified formulae, in the context of standard δ-rules based on Skolem terms. Structural results coming out from such mapping process are discussed.

In this paper we present a three valued many sorted logic for dealing with preorders, incorporating subsort relations into the syntax of the language, and where formulas taking the third boolean value as interpretation contain a term or a predicate not well-sorted w.r.t. the signature. For this logic a ground tableau-based deduction method and a free variable extension version are proposed, pro...

We present a sound, complete, modular and lean labelled tableau calculus for many propositional modal logics where the labels contain \free" and \universal" variables. Our \lean" Prolog implementation is not only surprisingly short, but compares favourably with other considerably more complex implementations for modal deduction.

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. ...