The last few years have seen the advent of a new breed of decision procedures for various fragments of first-order logic based on propositional abstraction. A lazy satisfiability checker for a given fragment of first-order logic invokes a theory-specific decision procedure (a theory solver) on a (partial) model for the abstraction. If the model is found to be consistent in the given theory, the...

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...

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 the area of fuzzy logic, expansions these logics by $\Delta$ operator have been intensively studied; interest is due to fact that it presents a behavior, associated systems were studied in propositional and first-order level. On other hand, possibility operators define Łukasiewicz-Moisil algebras over different classes algebras; are known as Moisil's literature. One coincides with $\Delta$, ...

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...