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Preface to First order theorem proving

2003
*
Journal of symbolic computation
*

*logic*, specialized

*decision*

*procedures*, strategies and complexity of theorem proving

*procedures*, and applications of first-order theorem provers to problems

*in*verification, artificial intelligence, and ... The call for papers mentions interest

*in*first-order classical, many-valued and modal

*logics*, resolution,

*equational*reasoning, term-rewriting, model

*construction*, constraint reasoning, unification, propositional ... A new

*decision*

*procedure*for a sub-fragment of the related Guarded Fragment is obtained by Lila Georgieva, Ullrich Hustadt and Renate A. Schmidt

*in*their paper Hyperresolution for guarded formulae. ...

##
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Page 2376 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
*
Mathematical Reviews
*

A

*clausal**logic*is defined*in*Section 2, and a*procedure*transforming any first-order formula into*clausal*form is presented. ... Clause graphs, which extend slightly the connection graph proof*procedure*of Kowalsky, are chosen*in*Section 4 to represent*logical*state transition systems. ...##
###
Page 9526 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

Summary: “This paper discusses the problem of how to transform a first-order formula into

*clausal*normal form, and to simultane- ously*construct*a proof that the*clausal*normal form is correct. ...*procedure*for guarded*logic*. ...##
###
An Experimental Evaluation of Ground Decision Procedures
[chapter]

2004
*
Lecture Notes in Computer Science
*

There is a large variety of algorithms for ground

doi:10.1007/978-3-540-27813-9_13
fatcat:vtodfjv6mrcknhl4vghsmdxvti
*decision**procedures*, but their differences,*in*particular*in*terms of experimental performance, are not well studied. ... We develop maps of the behavior of ground*decision**procedures*by comparing the performance of a variety of technologies on benchmark suites with differing characteristics. ...*In*eager approaches to*constructing*a GDP from a*decision**procedure*for T , propositional constraints formulas are transformed into equisatisfiable propositional formulas. ...##
###
Maximum Entropy modeling with Clausal Constraints
[chapter]

1997
*
Lecture Notes in Computer Science
*

*In*comparison with other inductive

*logic*programming systems, Maccent seems to be the rst that explicitly

*constructs*a conditional probability distribution p(CjI) based on an empirical distributioñ p(CjI ... Maccent incorporates

*clausal*constraints that are based on the evaluation of Prolog clauses

*in*examples represented as Prolog programs. ... Acknowledgements Luc Dehaspe is supported by the ESPRIT IV project no. 20237 on Inductive

*Logic*Programming II (ILP 2 ). ...

##
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First-Order Resolution Methods for Modal Logics
[chapter]

2013
*
Lecture Notes in Computer Science
*

*In*addition to traditional propositional modal

*logics*we consider more expressive PDL-like dynamic modal

*logics*which are closely related to description

*logics*. ...

*In*this paper we give an overview of results for modal

*logic*which can be shown using techniques and methods from first-order

*logic*and resolution. ... R with condensing is a

*decision*

*procedure*for (i) the

*clausal*form of the basic path

*logic*, and (ii) the

*clausal*form of the π of ′ fragment for K (D ) (m) . ...

##
###
Page 3869 of Mathematical Reviews Vol. , Issue 97F
[page]

1997
*
Mathematical Reviews
*

’s algorithm: a constraint-based completion

*procedure*(285-301); Dexter Kozen, Set constraints and*logic*programming (302-303); Witold Charatonik, Set con- straints*in*some*equational*theories (304-319 ...*In*Chapter 5 we discuss methods for automating systems of*logic*, both propositional and predicate. The reduction of formu- lae to prenex and*clausal*forms is described. ...##
###
Mechanised Reasoning and Model Generation for Extended Modal Logics
[chapter]

2003
*
Lecture Notes in Computer Science
*

We review and discuss the development of

doi:10.1007/978-3-540-24615-2_3
fatcat:jypyr3tokzhh7erjlyu5faipsi
*decision**procedures*for decidable extended modal*logics*and look at methods for automatically generating models. ... We focus on a class of extended modal*logics*very similar*in*spirit to propositional dynamic*logic*and closely related to description*logics*. ... By*constructing**decision**procedures*for these decidable fragments, one obtains generic*decision**procedures*for modal*logics*and the corresponding description*logics*. ...##
###
Clausal Connection-Based Theorem Proving in Intuitionistic First-Order Logic
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/11554554_19
fatcat:aacmbps255d7jo62s53bugoaxe
*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. The calculus was implemented by extending the classical prover leanCoP. ... The resulting implementation is able to refute a large set of first-order formulae (but it does not result*in*a*decision**procedure*for propositional formulae). ...##
###
The complexity of resource-bounded first-order classical logic
[chapter]

1994
*
Lecture Notes in Computer Science
*

We also show that the same problem when the initial formula is a set of Horn clauses is only NP-complete, and examine the case of rst-order

doi:10.1007/3-540-57785-8_131
fatcat:5qqepyy4qvbttfovupptc6ohjq
*logic*modulo an*equational*theory. ... Topics: computational complexity,*logics*, computational issues*in*AI (automated theorem proving). ...*In*contrast, linear*logic*, although based on resource-bounding ideas, is unsuited to automatic proof discovery. ...##
###
Page 3952 of Mathematical Reviews Vol. , Issue 92g
[page]

1992
*
Mathematical Reviews
*

This paper presents a

*decision**procedure*for semi-unification based on techniques similar to those used*in*the Knuth-Bendix completion*procedure*. ... Summary: “This paper provides an approach to the treatment of fuzzy equality*in*first-order*logic*, especially*in*a theory*in*which only equality occurs as a predicate symbol (namely,*equational*theory) ...##
###
Page 6866 of Mathematical Reviews Vol. , Issue 90M
[page]

1990
*
Mathematical Reviews
*

The proposed method constitutes a new arithmetical

*decision**procedure*for modal*logic*. ... Matrix characterisations, being free of the specific redundancies met within the sequent-based proof search, can be used to formulate efficient*decision**procedures*for the propositional fragments of modal ...##
###
Page 2878 of Mathematical Reviews Vol. , Issue 2001E
[page]

2001
*
Mathematical Reviews
*

The

*procedure*terminates and it is complete*in*the sense that it returns a model for each satisfiable formula if it admits an*equational*model. ... As a result we get an EXP-LIN- TIME*decision*algorithm.” ...##
###
Improving the Robustness and Encoding Complexity of Behavioural Clones
[chapter]

2001
*
Lecture Notes in Computer Science
*

by cart and;

doi:10.1007/3-540-44795-4_4
fatcat:cbiqctrvo5dh5dt2py4v3kbozq
*clausal*theories induced by an Inductive*Logic*Programming (ILP) system. ... We have investigated the use of three different representations to encode the artificial controllers: univariate*decision*trees as induced by C4.5; multivariate*decision*and regression trees as induced ... For that purpose we used and Inductive*Logic*Programming (ILP) system called IndLog (Camacho 2000) and encode the controller components as*clausal*theories. ...##
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Verified heap theorem prover by paramodulation

2012
*
Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12
*

By machine-checked, we mean it has a proof

doi:10.1145/2364527.2364531
dblp:conf/icfp/StewartBA12
fatcat:bdihjfjz2vfsrhf3vy5zjhwnca
*in*Coq that when the prover says "valid", the checked entailment holds*in*a proved-sound separation*logic*for C minor. ... By purely functional, we mean it is implemented*in*Gallina, the pure functional programming language embedded*in*the Coq theorem prover. ... This work was supported*in*part by AFOSR grant FA9550-09-1-0138 and NSF grant CNS-0910448. ...
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