We investigate the problem of nding a computable witness for the exis-tential quantiier in a formula of the classical rst-order predicate logic. The A-resolution calculus based on the program derivation algorithm A of C-L. Chang, R. C-T. Lee and R.Waldinger is used for nding a deenite substitution t for an existentially bound variable y in some formula F , such that F ft=yg is provable. The ter...

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that a...

A formal consideration in this paper is given for the essential notations to characterize the object that is distinguished in a problem domain. The distinct object is represented by another idealized object, which is a schematic element. When the existence of an element is significant, then a class of these partial elements is dropped down into actual, potential and virtual objects. The potenti...

B Proofs 3 B.1 Well-Formed Types and Environments . . . . . . . 3 B.2 Subtyping Inversion Lemma . . . . . . . . . . . . 3 B.3 Store Typing . . . . . . . . . . . . . . . . . . . . . 4 B.4 Values Inversion Lemma . . . . . . . . . . . . . . 6 B.5 Substitution . . . . . . . . . . . . . . . . . . . . . 9 B.6 Free Variables Lemma . . . . . . . . . . . . . . . 12 B.7 Well-Form Lemmas . . . . . . . . ....

We analyze the logical form of the domain knowledge that grounds analogical inferences and generalizations from a single instance. The form of the assumptions which justify analogies is given schematically as the "determination rule", so called because it expresses the relation of one set of variables determining the values of another set. The determination relation is a logical generalization ...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...

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...