In this paper, we introduce a new fragment of the rst-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satissability problem for monodic formulas in various linear time structures can be reduced to the satissability problem for a certain fragment of classical rst-order...

In this work we present FREEP 1.0, a theorem prover for the KLM preferential logic P of nonmonotonic reasoning. FREEP 1.0 is a SICStus Prolog implementation of a free-variables, labelled tableau calculus for P, obtained by introducing suitable modalities to interpret conditional assertions. The performances of FREEP 1.0 are promising. FREEP 1.0 can be downloaded at http:// www.di.unito.it/∼pozz...

We present a Prolog program that implements a sound and complete theorem prover for rst-order intuitionistic logic. It is based on free-variable semantic tableaux extended by an additional string uniica-tion to ensure the particular restrictions in intuitionistic logic. Due to the modular treatment of the diierent logical connectives the implementation can easily be adapted to deal with other n...

Reduction Stefano Guerrini July 20, 1999 In the -calculus, the -reduction ( x:MN) ! M[N=x] replaces each occurrence of the bound variable x in M by a copy of the argument N. This operation could obviously duplicate work, since any reduction required to simplify the argument will be repeated on each copy. At rst glance, it could seem that by choosing an innermost reduction strategy (i.e., reduci...

A refutation mechanism is introduced into logic programming, dual to the usual proof mechanism; then negation is treated via refutation. A four-valued logic is appropriate for the semantics: true, false, neither, both. Inconsistent programs are allowed, but inconsistencies remain localized. The four-valued logic is a well-known one, due to Belnap, and is the simplest example of Ginsberg’s bilat...

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various ...

The generic pronoun one (or its empty counterpart, arbitrary PRO) exhibits a range of properties that show a special connection to the first person, or rather the relevant intentional agent (speaker, addressee, or described agent). Generic one typically leads to generic sentences whose generalization is obtained from a first-person experience or action or else is meant to be immediately applica...

We present a completion-based method for handling a new version of E-unification, called “mixed” E-unification, that is a combination of the classical “universal” E-unification and “rigid” E-unification. Rigid E-unification is an important method for handling equality in Gentzen-type first-order calculi, such as free-variable semantic tableaux or matings. The performance of provers using E-unif...

Incremental closure is a proof search technique for free variable analytic tableaux where partial solutions are updated along with tableaux expansion. In this paper we address possible adaptations of the incremental closure technique to variable splitting tableaux. Variable splitting tableaux provide a sound way to instantiate occurrences of the same variable in different branches differently b...

We provide a partial survey of three approaches to two problems in the semantics of person, which we call the ‘Bindability Problem’ and the ‘Shiftability Problem’. On the standard (Kaplanian) view of indexical pronouns, the semantic value of I and you is determined by a context rather than by an assignment function [=Separation Thesis], and furthermore this context must be that of the actual sp...