Results 71 to 80 of about 307,150 (181)

Proof Generation from Delta-Decisions

, 2014
We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision procedures.
Clarke, Edmund, Gao, Sicun, Kong, Soonho
core   +1 more source

Superposition and chaining for totally ordered divisible abelian groups

, 2001
We present a calculus for first-order theorem proving in the presence of the axioms of totally ordered divisible abelian groups. The calculus extends previous superposition or chaining calculi for divisible torsion-free abelian groups and dense total ...
Waldmann, U.
core  

How to Prove Higher Order Theorems in First Order Logic [PDF]

, 1999
In this paper we are interested in using a first order theorem prover to prove theorems that are formulated in some higher order logic. To this end we present translations of higher order logics into many sorted first order logic with equality and give a sufficient criterion for the soundness of these translations.
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Explaining the undecidability of first-order logic

Zagadnienia Filozoficzne w Nauce
Turing proved the unsolvability of the decision problem for first-order logic (Entscheidungsproblem) in his famous paper On Computable Numbers, with an Application to the Entscheidungsproblem.
Timm Lampert, Anderson Nakano
doaj   +1 more source

Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic [PDF]

, 2005
We present a clausal connection calculus for first-order intuitionistic logic. It extends the classical connection calculus by adding prefixes that encode the characteristics of intuitionistic logic. Our calculus is based on a clausal matrix characterisation for intuitionistic logic, which we prove correct and complete.
openaire   +1 more source

A conservative extension of first-order logic and its applications to theorem proving

, 1993
We define a weak second-order extension of first-order logic. We prove a second-order cut elimination theorem for this logic and use this to prove a conservativity and a realisability result. We give applications to formal program development and theorem proving, in particular, in modeling techniques in formal metatheory.
Basin, D., Matthews, S.
openaire   +3 more sources

First-order theorem proving: Foreword

Journal of Symbolic Computation, 2012
Peltier, N., Sofronie-Stokkermans, V.
openaire   +2 more sources

Instantiation-based First-Order Theorem Proving with Equality

, 2023
Instantiation-based methods have shown great results in automated first-order theorem proving, especially in the decidable and effectively propositional fragment of first-order logic. However, it has been demonstrated that the successful and simple search for pairs of clashing literals is not sufficient with equational literals.
openaire   +1 more source

First-order theorem proving modulo equations

, 1992
We present refutationally complete calculi for first-order clauses with equality. General paramodulation calculi cannot efficiently deal with equations such as associativity and commutativity axioms. Therefore we will separate a set of equations (called {$E$}-equations) from a specification and give them a special treatment, avoiding paramodulations ...
openaire   +1 more source

On Spectrum of kappa-Resplendent Models

, 2011
We prove that some natural "outside" property is equivalent (for a first order class) to being stable. For a model, being resplendent is a strengthening of being kappa-saturated. Restricting ourselves to the case kappa > |T| for transparency, a model M
Shelah, Saharon
core