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.

We analyze, along the lines of the knowledge compilation map, both the tractability and the succinctness of the propositional language URC-C of unit-refutation complete propositional formulae, as well as its disjunctive closure URC-C[∨, ∃], and a superset of URC-C where variables can be existentially quantified and unitrefutation completeness concerns only consequences built up from free variab...

A theory satis es the k variable property if every rst order formula is equivalent to a formula with at most k bound variables possibly reused Gabbay has shown that a model of temporal logic satis es the k variable property for some k if and only if there exists a nite basis for the temporal connectives over that model We give a model theoretic method for establishing the k variable property in...

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 study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are decidable, and that rewritability into Datalog is decidable when the original query satisfies a certa...

Generic rst-order logic (GFOL) is a rst-order logic parameterized with terms de ned axiomatically (rather than constructively), by requiring them to only provide generic notions of free variable and substitution satisfying reasonable properties. GFOL has a complete Gentzen system generalizing that of FOL. An important fragment of GFOL, called HORN, possesses a much simpler Gentzen system, simil...

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.

Finding appropriate bound sets of variables is the most important task of functional decomposition. When solving some problems the bound sets need to be large; for instance in decomposition to symmetric subfunctions realized in MOPS arrays for submicron technologies, or when no good small bound sets exist. In such cases the creation of the incompatibility graph, that is necessary to evaluate go...

This paper analyses inherent clitics of idiomatic constructions as verbal arguments (Jelinek 1984, Baker 1996, Hale 2003) that are translated as free variables (Delfitto 2002): they are anaphoric to a (hidden) non-referential discourse topic or (right) dislocated constituent. Furthermore, since they denote abstract semantic objects (Asher 1993), they are assumed to be semantically incorporated ...

In a bounded analysis, arithmetic operators become partial, and a different semantics becomes necessary. One approach, mimicking programming languages, is for overflow to result in wrap-around. Although easy to implement, wrap-around produces unexpected counterexamples that do not correspond to cases that would arise in the unbounded setting. This paper describes a new approach, implemented in ...