This work describes the proof and uses of a theorem allowing definition of recursive functions over the type of λ-calculus terms, where terms with bound variables are identified up to α-equivalence. The theorem embodies what is effectively a principle of primitive recursion, and the analogues of this theorem for other types with binders are clear. The theorem’s side-conditions require that the ...

‖ The methods that were used to prove the consistency of formalized theories from the finitist standpoint can be surveyed according to the following classification. ‖1. Method of valuation. It has obtained its essential development by Hilbert’s procedure of trial valuation. Using this procedure Ackermann and v. Neumann demonstrated the consistency of number theory—admittedly, under the restrict...

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 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.

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...