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

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*. ...

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

2018
*
Lecture Notes in Computer Science
*

Running example:

doi:10.1007/978-3-319-94205-6_13
fatcat:cemgamgrabfh5bqcehoesszg6q
*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. ...##
###
Little Engines of Proof
[chapter]

2002
*
Lecture Notes in Computer Science
*

The other school, pioneered by Hao Wang, argues

doi:10.1007/3-540-45614-7_1
fatcat:6my3fmm6xjb4vfj6sxly46xbxa
*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*. ...##
###
CVC: A Cooperating Validity Checker
[chapter]

2002
*
Lecture Notes in Computer Science
*

CVC implements

doi:10.1007/3-540-45657-0_40
fatcat:lbitv5wtmzcyviczsumygptaia
*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] . ...##
###
The UCLID Decision Procedure
[chapter]

2004
*
Lecture Notes in Computer Science
*

UCLID is

doi:10.1007/978-3-540-27813-9_40
fatcat:b764wtws7ner7epgz4izhx674y
*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. ...##
###
Rewriting, Inference, and Proof
[chapter]

2010
*
Lecture Notes in Computer Science
*

Rewriting is

doi:10.1007/978-3-642-16310-4_1
fatcat:vqoukc27wnhtrdsvcr2hymspt4
*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. ...##
###
Saturation-based theorem proving: Past successes and future potential
[chapter]

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*...

##
###
Forthcoming Papers

2002
*
Journal of Logic and Computation
*

This paper contains

doi:10.1093/logcom/12.5.911
fatcat:uba4ocmuhrfvrdxxxdgytudoee
*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*. ...##
###
Logic for computer science

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 ...

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

2011
*
Lecture Notes in Computer Science
*

We thereby obtain high correctness assurances

doi:10.1007/978-3-642-25379-9_15
fatcat:gesxkp2cm5girliosyngzyuwmi
*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. ...##
###
Kanger's Choices in Automated Reasoning
[chapter]

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. ...

##
###
Proof Generation in CDSAT

2021
*
Electronic Proceedings in Theoretical Computer Science
*

The main ideas in the CDSAT (Conflict-Driven Satisfiability) framework

doi:10.4204/eptcs.336.1
fatcat:ch2h4j3pdndpxmgigudnlrlauu
*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*. ...##
###
Tableau-based Decision Procedure for Non-Fregean Logic of Sentential Identity
[chapter]

2021
*
Lecture Notes in Computer Science
*

To the best of our knowledge, it is the first implemented

doi:10.1007/978-3-030-79876-5_3
fatcat:kvlragf4qnbo5pirpvyvwl2xu4
*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*. . . ...##
###
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

2007
*
Proceedings of the second workshop on Automated formal methods - AFM '07
*

In order to make

doi:10.1145/1345169.1345176
fatcat:k6tzizy3lzciho5az7rmka2xu4
*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*. ...
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