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A Proof System and a Decision Procedure for Equality Logic [chapter]

Olga Tveretina, Hans Zantema
2004 Lecture Notes in Computer Science  
a general theorem globalizing a local commutation criterion for different proof systems.  ...  We give an approach for deciding satisfiability of equality logic formulas (E-SAT) in conjunctive normal form. Central in our approach is a single proof rule called equality resolution (ER).  ...  [2] proposed a decision procedure based on computing congruence closure in combination with case splitting. Many approaches use transformation of equality logic to propositional logic.  ... 
doi:10.1007/978-3-540-24698-5_56 fatcat:dzbddayy2vc25ctgfganrhpft4

A Why3 Framework for Reflection Proofs and Its Application to GMP's Algorithms [chapter]

Guillaume Melquiond, Raphaël Rieu-Helft
2018 Lecture Notes in Computer Science  
Running example: systems of linear equalities As an example, let us consider a decision procedure for linear equation systems in an arbitrary field (code excerpts in Figure 3 ).  ...  Second, we have implemented and verified a procedure for automatically solving systems of linear equalities with symbolic coefficients.  ... 
doi:10.1007/978-3-319-94205-6_13 fatcat:cemgamgrabfh5bqcehoesszg6q

Little Engines of Proof [chapter]

Natarajan Shankar
2002 Lecture Notes in Computer Science  
The other school, pioneered by Hao Wang, argues for problem-specific combinations of decision and semi-decision procedures.  ...  In recent years, several high quality inference engines have been developed, including propositional satisfiability solvers, ground decision procedures for equality and arithmetic, quantifier elimination  ...  Many theorem proving systems are based around decision procedures for equality.  ... 
doi:10.1007/3-540-45614-7_1 fatcat:6my3fmm6xjb4vfj6sxly46xbxa

CVC: A Cooperating Validity Checker [chapter]

Aaron Stump, Clark W. Barrett, David L. Dill
2002 Lecture Notes in Computer Science  
CVC implements a framework for combining subsidiary decision procedures for certain logical theories into a decision procedure for the theories' union.  ...  Decision procedures for decidable logics and logical theories have proven to be useful tools in verification. This paper describes the CVC ("Cooperating Validity Checker") decision procedure.  ...  with equality can be combined to obtain a decision procedure for the union of the theories [7] .  ... 
doi:10.1007/3-540-45657-0_40 fatcat:lbitv5wtmzcyviczsumygptaia

The UCLID Decision Procedure [chapter]

Shuvendu K. Lahiri, Sanjit A. Seshia
2004 Lecture Notes in Computer Science  
UCLID is a tool for term-level modeling and verification of infinite-state systems expressible in the logic of counter arithmetic with lambda expressions and uninterpreted functions (CLU).  ...  In this paper, we describe a key component of the tool, the decision procedure for CLU.  ...  Bryant for his invaluable support and feedback.  ... 
doi:10.1007/978-3-540-27813-9_40 fatcat:b764wtws7ner7epgz4izhx674y

Rewriting, Inference, and Proof [chapter]

Natarajan Shankar
2010 Lecture Notes in Computer Science  
Rewriting is a form of inference, and one that interacts in several ways with other forms of inference such as decision procedures and proof search.  ...  We discuss these problems in the context of our ongoing effort to use PVS as a metatheoretic framework to construct a proof kernel for justifying the claims of theorem provers, rewriters, model checkers  ...  Inference systems can be given for a variety of decision procedures including SAT and SMT solvers.  ... 
doi:10.1007/978-3-642-16310-4_1 fatcat:vqoukc27wnhtrdsvcr2hymspt4

Saturation-based theorem proving: Past successes and future potential [chapter]

Harald Ganzinger
1996 Lecture Notes in Computer Science  
Proof-search in intuitionistic logic with equality, or back to simultaneous rigid E-Unification p. 32 Extensions to a generalization critic for inductive proof p. 47 Learning domain knowledge to improve  ...  recursive procedures p. 201 FasTraC: a decentralized traffic control system based on logic programming p. 216 Presenting machine-found proofs p. 221 MUltlog 1.0: towards an expert system for  ... 
doi:10.1007/3-540-61511-3_64 fatcat:iizfu32trnfadmj4z7xcvwds5y

Forthcoming Papers

2002 Journal of Logic and Computation  
This paper contains a description of a decision algorithm SCU for stratified context unification together with a proof of its correctness, which shows decidability of stratified context unification as  ...  The relevance principle does not hold for substructural logics with mingle and usual negation, but holds for those with mingle and strong negation.  ...  Using such calculi we define a Ç´Òµ-SPACE decision procedure for the second logic and a Ç´Ò ÐÓ Òµ-SPACE decision procedure for each of the other two logics.  ... 
doi:10.1093/logcom/12.5.911 fatcat:uba4ocmuhrfvrdxxxdgytudoee

Logic for computer science

Ursula Martin
1988 Science of Computer Programming  
A theorem prover may contain an efficient implementation of a decision procedure or semidecision procedure, or it may rely on the user to build up a proof or an outline of a proof, which it then checks  ...  Many theorem provers, and the programming language PROLOG, use the resolution procedure, a demi-decision procedure for the first order predicate calculus which has its roots in work of Herbrand in 1930  ... 
doi:10.1016/0167-6423(88)90006-8 fatcat:vgyaht6uifaq7puyk5lcdtlrc4

Reconstruction of Z3's Bit-Vector Proofs in HOL4 and Isabelle/HOL [chapter]

Sascha Böhme, Anthony C. J. Fox, Thomas Sewell, Tjark Weber
2011 Lecture Notes in Computer Science  
We thereby obtain high correctness assurances for Z3's results, and increase the degree of proof automation for bit-vector problems in HOL4 and Isabelle/HOL.  ...  We present independent reconstruction of unsatisfiability proofs for bit-vector theories in the theorem provers HOL4 and Isabelle/HOL.  ...  The authors are grateful to Nikolaj Bjørner and Leonardo de Moura for their help with Z3.  ... 
doi:10.1007/978-3-642-25379-9_15 fatcat:gesxkp2cm5girliosyngzyuwmi

Kanger's Choices in Automated Reasoning [chapter]

Anatoli Degtyarev, Andrei Voronkov
2001 Collected Papers of Stig Kanger with Essays on His Life and Work  
A sequent-based proof procedure for logic with functional symbols and equality w as described in Kanger 1959 ] and Kanger 1963] .  ...  ) Gentzen 1934] was the rst to describe a decision procedure for propositional intuitionistic logic as proof-search in his cut-free calculus.  ... 
doi:10.1007/978-94-010-0630-9_4 fatcat:3sd5mf3k5bcbloyxjniit4avdq

Proof Generation in CDSAT

Maria Paola Bonacina
2021 Electronic Proceedings in Theoretical Computer Science  
The main ideas in the CDSAT (Conflict-Driven Satisfiability) framework for SMT are summarized, leading to approaches to proof generation in CDSAT.  ...  Acknowledgements The author thanks Stéphane Graham-Lengrand for their discussions.  ...  An inference system is a set of inference rules, and a theory module is an abstraction of a satisfiability procedure.  ... 
doi:10.4204/eptcs.336.1 fatcat:ch2h4j3pdndpxmgigudnlrlauu

Tableau-based Decision Procedure for Non-Fregean Logic of Sentential Identity [chapter]

Joanna Golińska-Pilarek, Taneli Huuskonen, Michał Zawidzki
2021 Lecture Notes in Computer Science  
To the best of our knowledge, it is the first implemented decision procedure for $$\mathsf {SCI}$$ SCI which runs in NP, i.e., is complexity-optimal.  ...  We describe an implementation of the procedure and compare its performance with implementations of other calculi for $$\mathsf {SCI}$$ SCI (for which, however, the termination results were not established  ...  Tableau-based Decision Procedure for Non-Fregean Logic. . .  ... 
doi:10.1007/978-3-030-79876-5_3 fatcat:kvlragf4qnbo5pirpvyvwl2xu4

Page 6089 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
(4-WARW-C; Coventry) A proof system for finite trees.  ...  A decision procedure based on the basic calculus is devised and then it is extended to minimal model inference. The basic decision procedure and its extension enjoy some interesting properties.  ... 

Lightweight integration of the Ergo theorem prover inside a proof assistant

Sylvain Conchon, Evelyne Contejean, Johannes Kanig, Stéphane Lescuyer
2007 Proceedings of the second workshop on Automated formal methods - AFM '07  
In order to make a sound integration in a proof assistant possible, Ergo is capable of generating proof traces for CC(X).  ...  Ergo is a little engine of proof dedicated to program verification. It fully supports quantifiers and directly handles polymorphic sorts.  ...  On the one hand, Coq's rich higherorder logics is not well-adapted to decision procedures that were designed for first order logics.  ... 
doi:10.1145/1345169.1345176 fatcat:k6tzizy3lzciho5az7rmka2xu4
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