The property of Positive Equality [2] dramatically speeds up validity checking of formulas in the logic of Equality with Uninterpreted Functions and Memories (EUFM) [4]. The logic expresses correctness of high-level microprocessors. We present EVC (Equality Validity Checker)—a tool that exploits Positive Equality and other optimizations when translating a formula in EUFM to a propositional form...

We present a fragment of predicate logic which allows the use of equality and quantification but whose models are limited to finite Herbrand interpretations. Formulae in this logic can be thought as syntactic sugar on top of the Bernays-Schönfinkel fragment and can, therefore, still be effectively grounded into a propositional representation. We motivate the study of this logic by showing that ...

Preliminaries abstract reduction systems well-founded orderings Propositional logic syntax, semantics calculi: DPLL-procedure, . . . implementation: 2-watched literals, clause learning First-order predicate logic syntax, semantics, model theory, . . . calculi: resolution, tableaux, . . . implementation: sharing, indexing First-order predicate logic with equality term rewriting systems calculi: ...

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

In using the logic of equality with unininterpreted functions to verify hardware systems, specific characteristics of the formula describing the correctness condition can be exploited when deciding its validity. We distinguish a class of terms we call “p-terms” for which equality comparisons can appear only in monotonically positive formulas. By applying suitable abstractions to the hardware mo...

In this work, we attempt to alleviate three (more or less) equivalent negative results. These are (i) non-axiomatizability (by any finite schema) of the valid formula schemas of first order logic, (ii) non-axiomatizability (by finite schema) of any propositional logic equivalent with classical first order logic (i.e., modal logic of quantification and substitution), and (iii) non-axiomatizabili...

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E . In contrast to the wellknown interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE , but rather by a suitable complete Heyting algebra H . The canonical map relating H and ΩE both serves to interpret equality and provides a modal...