In this paper, we introduce a new fragment of the first-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 satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for a certain fragment of classical first...

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...

Œough systems with process creation give rise to unboundedly many processes, their names are systematically generated and typically form a regular set. When we consider modal logics to specify properties of such systems, it is natural to consider quanti€cation over such regular sets. Œese are in the realm of term modal logics, which are usually undecidable. We consider themonodic variant, in wh...

In this paper we propose a new type of “image” representation for periodic behaviors and analyze the relationship between image representability and controllability, showing that the correspondence, which exists in the time-invariant case, generalizes to periodic behaviors. We also show that the concept of free variable used in the time-invariant case cannot be transposed to the periodic case i...

Part one is a supplement to papers [1], [2], and [3]. It deals with concepts of selector functions, atomic, negative, conjunctive formulas and etc., subformulas, free variables, satisfiability and models (it is shown that axioms of the predicate and the quantifier calculus are satisfied in an arbitrary set). In part two there are introduced notions of variables occurring in a formula and replac...

We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not...

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.

We present a formal method of functional program develop ment based on step by step transformation In their most abstract form speci cations are essentially predicates that relate the result of the speci ed program to the free variables of that pro gram In their most concrete form speci cations are simply programs in a functional programming language Development from abstract speci cations to p...

We address the problem of complementing higher-order patterns without repetitions of free variables. Diierently from the rst-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a nite set of patterns. We therefore generalize the simply-typed-calculus to include an internal notion of strict function so that we can directly express that a term must de...