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Theorem Proving Modulo
 Journal of Automated Reasoning
"... Abstract. Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of much wider interest because it permits to separate computations and deductions in a clean way. The first ..."
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Cited by 111 (18 self)
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contribution of this paper is to define a sequent calculus modulo that gives a proof theoretic account of the combination of computations and deductions. The congruence on propositions is handled via rewrite rules and equational axioms. Rewrite rules apply to terms and also directly to atomic propositions
Variant Narrowing and Equational Unification
 In Proc. of WRLA 2008, ENTCS
, 2009
"... Abstract. Narrowing is a wellknown complete procedure for equational Eunification when E can be decomposed as a union E = ∆ ⊎ B with B a set of axioms for which a finitary unification algorithm exists, and ∆ a set of confluent, terminating, and Bcoherent rewrite rules. However, when B ̸ = ∅, ef ..."
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Cited by 13 (7 self)
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= ∅, efficient narrowing strategies such as basic narrowing easily fail to be complete and cannot be used. This poses two challenges to narrowingbased equational unification: (i) finding efficient narrowing strategies that are complete modulo B under mild assumptions on B, and (ii) finding sufficient conditions
Conditional Narrowing Modulo in Rewriting Logic and Maude?
"... Abstract. This work studies the relationship between verifiable and computable answers for reachability problems in rewrite theories with an underlying membership equational logic. These problems have the form (∃x̄)s(x̄) → ∗ t(x̄), with x ̄ some variables, or a conjunction of several of these subgoa ..."
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Abstract. This work studies the relationship between verifiable and computable answers for reachability problems in rewrite theories with an underlying membership equational logic. These problems have the form (∃x̄)s(x̄) → ∗ t(x̄), with x ̄ some variables, or a conjunction of several
OrderSorted Equality Enrichments Modulo Axioms
"... Abstract. Builtin equality and inequality predicates based on comparison of canonical forms in algebraic specifications are frequently used because they are handy and efficient. However, their use places algebraic specifications with initial algebra semantics beyond the pale of theorem proving tool ..."
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specification E to a specification E ≃ where equationallydefined equality predicates have been added? This paper answers this question in the affirmative for a broad class of ordersorted conditional specifications E that are sortdecreasing, ground confluent, and operationally terminating modulo axioms B
Proofs in Satisfiability Modulo Theories
"... Satisfiability Modulo Theories (SMT) solvers4 check the satisfiability of firstorder formulas written in a language containing interpreted predicates and functions. These interpreted symbols are defined either by firstorder axioms (e.g. the axioms of equality, or array axioms for operators read a ..."
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Cited by 2 (1 self)
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Satisfiability Modulo Theories (SMT) solvers4 check the satisfiability of firstorder formulas written in a language containing interpreted predicates and functions. These interpreted symbols are defined either by firstorder axioms (e.g. the axioms of equality, or array axioms for operators read
UNIFICATION MODULO A 2SORTED EQUATIONAL THEORY
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Logical Methods in Computer Science Vol. 10(1:5)2014, pp. 1–26 www.lmcsonline.org
Incremental Checking of WellFounded Recursive Specifications Modulo Axioms
, 2011
"... We introduce the notion of wellfounded recursive ordersorted equational logic (OS) theories modulo axioms. Such theories define functions by wellfounded recursion and are inherently terminating. Moreover, for wellfounded recursive theories important properties such as confluence and sufficient c ..."
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We introduce the notion of wellfounded recursive ordersorted equational logic (OS) theories modulo axioms. Such theories define functions by wellfounded recursion and are inherently terminating. Moreover, for wellfounded recursive theories important properties such as confluence and sufficient
Deduction modulo theory
"... 1.1 Weaker vs. stronger systems Contemporary proof theory goes into several directions at the same time. One of them aims at analysing proofs, propositions, connectives, etc., that is at decomposing them into more atomic objects. This often leads to design systems ..."
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1.1 Weaker vs. stronger systems Contemporary proof theory goes into several directions at the same time. One of them aims at analysing proofs, propositions, connectives, etc., that is at decomposing them into more atomic objects. This often leads to design systems
Conditional Directed Narrowing
, 1996
"... . We present an implementation of directed narrowing extended to the conditional framework, which is complete for two classes of conditional term rewrite systems : confluent and decreasing on one hand, levelconfluent and terminating on the other hand. 1 Introduction Narrowing was originally in ..."
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of equational Horn clauses, i.e. a conditional term rewrite system (CTRS). However, conditional narrowing is inefficient for practical applications because the search space is huge and contains infinite branches. This is why many authors have proposed optimizations to the narrowing procedure : innermost, basic
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