Tree-width for first order formulae

Tree-Width for First Order Formulae

We introduce tree-width for first order formulae φ, fotw(φ). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed parameter tractable, with parameter the length of the formula. This is done by translating a formula φ with fotw(φ) < k into a formula of the k-variable fragment L of firs...

A Normal Form for First-Order Temporal Formulae

In this paper a normal form for formulae of a first-order temporal logic is described. This normal form, called First-Order Separated Normal Form (SNFƒ), forms the basis of both a temporal resolution method [5] and a family of executable temporal logics [2]. A firstorder temporal logic, based on a linear discrete model structure, is introduced and the procedure for transforming an arbitrary for...

Formal Topologies on The Set of First-Order Formulae

Variables in Formulae of the First Order Language 1

The articles [7], [5], [9], [8], [3], [4], [2], [6], and [1] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: i, j, k denote natural numbers, x denotes a bound variable, a denotes a free variable, p, q denote elements of WFF, l denotes a finite sequence of elements of Var, P denotes a predicate symbol, and V denotes a non empty subset of Va...

Monadic Second Order Finite Satisfiability and Unbounded Tree-Width

The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese [24]. We prove that the following problem is decidable: Input: (i) A monadic second order logic sentence α, and (ii) a sentence β in the two-variable fragment of first order logic extended with counting quantifiers. The vocabularies of α...