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Preface to First order theorem proving

Peter Baumgartner, Hantao Zhang
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.  ... 
doi:10.1016/s0747-7171(03)00022-1 fatcat:lcsgf3vtb5hqbhn3rhihhpbkku

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]

Leonardo de Moura, Harald Rueß
2004 Lecture Notes in Computer Science  
There is a large variety of algorithms for ground 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.  ... 
doi:10.1007/978-3-540-27813-9_13 fatcat:vtodfjv6mrcknhl4vghsmdxvti

Maximum Entropy modeling with Clausal Constraints [chapter]

Luc Dehaspe
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 ).  ... 
doi:10.1007/3540635149_39 fatcat:samvmfv46bdkppbu4e427pgwpi

First-Order Resolution Methods for Modal Logics [chapter]

Renate A. Schmidt, Ullrich Hustadt
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) .  ... 
doi:10.1007/978-3-642-37651-1_15 fatcat:pta3fxqsnfal3cigcnryyxjcba

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]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
We review and discuss the development of 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.  ... 
doi:10.1007/978-3-540-24615-2_3 fatcat:jypyr3tokzhh7erjlyu5faipsi

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

Jens Otten
2005 Lecture Notes in Computer Science  
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. 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).  ... 
doi:10.1007/11554554_19 fatcat:aacmbps255d7jo62s53bugoaxe

The complexity of resource-bounded first-order classical logic [chapter]

Jean Goubault
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 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.  ... 
doi:10.1007/3-540-57785-8_131 fatcat:5qqepyy4qvbttfovupptc6ohjq

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]

Rui Camacho, Pavel Brazdil
2001 Lecture Notes in Computer Science  
by cart and; 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.  ... 
doi:10.1007/3-540-44795-4_4 fatcat:cbiqctrvo5dh5dt2py4v3kbozq

Verified heap theorem prover by paramodulation

Gordon Stewart, Lennart Beringer, Andrew W. Appel
2012 Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12  
By machine-checked, we mean it has a proof 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.  ... 
doi:10.1145/2364527.2364531 dblp:conf/icfp/StewartBA12 fatcat:bdihjfjz2vfsrhf3vy5zjhwnca
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