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Page 749 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Anton Setzer (4-WALS-C; Swansea) 2004b:03019 03B20 03B35 68T15 Voronkoy, Andrei (S-UPPS-CS; Uppsala) Proof-search in intuitionistic logic with equality, or back to simultaneous rigid E-unification.  ...  This characterization un- covers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid E-unification.  ... 

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  ...  Proof search with set variable instantiation in the calculus of constructions p. 658Search strategies for resolution in temporal logics p. 673Optimal axiomatizations for multiple-valued operators and quantifiers  ... 
doi:10.1007/3-540-61511-3_64 fatcat:iizfu32trnfadmj4z7xcvwds5y

Page 3844 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
Giovanni Criscuolo (Naples) 2000f:03018 03B20 03B35 68T15 Voronkovy, Andrei (S-UPPS-CS; Uppsala) Proof search in intuitionistic logic with equality, or Back to simultaneous rigid E-unification.  ...  Algebra 115 (1997), no. 3, 241-274; MR 98a:03105; First-order logic with dependent sorts with applications to category theory, Lecture Notes in Logic, Springer, Berlin, to appear].  ... 

Monadic simultaneous rigid E-unification

Yuri Gurevich, Andrei Voronkov
1999 Theoretical Computer Science  
We study the monadic case of a decision problem known as simultaneous rigid E-unification. We show its equivalence to an extension of word equations.  ...  Acknowledgements Remarks of Margus Veanes allowed us to simplify several proofs, and especially that of Theorem 4. We also thank Anatoli Degtyarev and Gennadi Makanin.  ...  In this section we define simultaneous rigid E-unification, discuss its connection with several decision problems in logic, and survey some known results.  ... 
doi:10.1016/s0304-3975(98)00123-6 fatcat:4d7c5tlznbbwzoal6ikkd4avmy

Unification under a mixed prefix

Dale Miller
1992 Journal of symbolic computation  
Unification problems are identified with conjunctions of equations between simply typed X-terms where free variables in the equations can be universally or existentially quantified .  ...  The method of searching for pre-unifiers described by Huet is easily extended to the mixed prefix setting, although solving flexible-flexible unification problems is undecidable since types may be empty  ...  Fortunately, determining whether or not there is a Q-substitution given Q is decidable since it is equivalent to proving formulas in intuitionistic propositional logic .  ... 
doi:10.1016/0747-7171(92)90011-r fatcat:cqv3ltdrgrgfrdoxfo5qpv4ri4

Monadic simultaneous rigid E-unification and related problems [chapter]

Yuri Gurevich, Andrei Voronkov
1997 Lecture Notes in Computer Science  
We study the monadic case of a decision problem know as simultaneous rigid E-uni cation. We show its equivalence to an extension of word equations.  ...  We shall consider equational logic, i.e. logic whose only predicate is the equality predicate ', but our results can easily be generalized to general rst-order logic with equality.  ...  In this section we de ne simultaneous rigid E-uni cation, discuss its connection with several decision problems in logic and survey some known results.  ... 
doi:10.1007/3-540-63165-8_173 fatcat:scb74ggec5expfcu3jdct4vyxq

Elimination of Negation in a Logical Framework [chapter]

Alberto Momigliano
2000 Lecture Notes in Computer Science  
To bring this to the extreme, deductive systems can be expressed eventually in, say, first-order Horn logic and ideally proved-checked or even demonstrated by a resolution theorem prover or more likely  ...  However, this would not only significantly complicate goal-oriented proof search (as it is manifested in the difficulty of implementing, for example, the full logic of Forum [Mil94]), but providing negative  ...  . • Reduce the complexity of proof-search. • Inherit a treatable unification problem. 2.  ... 
doi:10.1007/3-540-44622-2_28 fatcat:hywfda5dhfhtdgf2lmigtjz4om

A Semantic Completeness Proof for TaMeD [chapter]

Richard Bonichon, Olivier Hermant
2006 Lecture Notes in Computer Science  
This new proof allows us to extend the completeness theorem to several classes of rewrite systems used for computations in deduction modulo.  ...  Deduction modulo is a theoretical framework designed to introduce computational steps in deductive systems.  ...  The proof of as simple a statement as (a + b) + ((c + d) + e) = a + ((b + c) + (d + e)) might take a long time within a theory with the usual associativity and identity axioms if one uses an ineffective  ... 
doi:10.1007/11916277_12 fatcat:msi6arkv5rdghmrjq4abs4p74u

On the logic of unification

Philippe Le Chenadec
1989 Journal of symbolic computation  
in unification logic.  ...  Unification, or solving equations on finite trees, is a P-complete problem central to symbolic manipulation, especially in Resolution, Type Inference and Rewriting.  ...  To be convinced of this fact, consider the proof search procedure in w Also, the detour by technical results is unavoidable for obtaining deep results on unification logic.  ... 
doi:10.1016/s0747-7171(89)80024-0 fatcat:ut7xzm7cwbdl3csakx4vldmc3m

An Implementation of the Language Lambda Prolog Organized around Higher-Order Pattern Unification [article]

Xiaochu Qi
2009 arXiv   pre-print
A key idea is the orientation of the computation model of Lambda Prolog around a restricted version of higher-order unification with nice algorithmic properties and appearing to encompass most interesting  ...  This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects  ...  that is equal to A r or to G ⊃ A r .  ... 
arXiv:0911.5203v1 fatcat:6d2kzgj6b5d5th6dhiijcv4mqe

Hybridizing a Logical Framework

Jason Reed
2007 Electronical Notes in Theoretical Computer Science  
Anything I've accomplished here is a footnote to time spent over lunches or at the whiteboards with Kevin, Brigitte, Aleks, Kaustuv, Tom, Donna, Spoons, Deepak, William, Chris, Neel, D, Noam, and Dan.  ...  More importantly, it makes it possible to realize a metalogical framework capable of reasoning about stateful deductive systems encoded in the style familiar from prior work with LLF, taking advantage  ...  of a BI proposition can in fact be mapped back to a BI proof.  ... 
doi:10.1016/j.entcs.2006.11.030 fatcat:uzgxb2zi5rdbhpzkfuojq5ccrq

Buying Logical Principles with Ontological Coin: The Metaphysical Lessons of Adding epsilon to Intuitionistic Logic

David DeVidi, Corey Mulvihill
2017 IfColog journal of logics and their applications (FLAP)  
This special issue of the Journal of Logics and their Applications follows a workshop organized in Montpellier in June 12-15 2015.  ...  We would like to thank Aïda Diouf and Elisabeth Gréverie from the University of Montpellier for their extremely valuable help with organisational issues.  ...  The authors would like to thank: Christian Retoré for organizing the workshop on Hilbert's Epsilon and Tau in Logic, Informatics and Linguistics; the anonymous reviewers of this workshop for providing  ... 
dblp:journals/flap/DeVidiM17 fatcat:r2sm6fbvtncsziyterc76pw46m

Scoping constructs in logic programming: Implementation problems and their solution

Gopalan Nadathur, Bharat Jayaraman, Keehang Kwon
1995 The Journal of Logic Programming  
When universal and existential quantifiers are permitted to appear in mixed order in goals, the devices of logic variables and unification that are employed in solving existential goals must be modified  ...  Suitable modifications that are based on attaching numerical tags to constants and variables and on using these tags in unification are described.  ...  If there is a derivation of G from P with answer substitution 0, then there is a proof in intuitionistic logic for O(G) from 7 9. 2.  ... 
doi:10.1016/0743-1066(95)00037-k fatcat:4ijzslrz6nbdrnell6sjjmhrry

The Coq Proof Assistant, version 8.10.0 [article]

The Coq Development Team
2019 Zenodo  
It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.  ...  The unfolding heuristic in termination checking was made more complete, allowing more constants to be unfolded to discover valid recursive calls. Performance regression [...]  ...  Usage The Coq Reference Manual, Release 8.10.0 default on NTFS (Windows) or HFS+ (MacOS X) file systems is on the contrary to disallow two files differing only in the case in the same directory.  ... 
doi:10.5281/zenodo.3476303 fatcat:nq2hvuywmre3xmbaqly2xxt6za

The History of Categorical Logic: 1963–1977 [chapter]

Jean-Pierre Marquis, Gonzalo E. Reyes
2012 Handbook of the History of Logic  
logic encodes first-order and higher-order logics (classical, intuitionistic, etc.) by categories with additional properties and structure (Boolean categories, Heyting categories and so on).  ...  Most readers would probably find more instructive to learn that categorical logic is algebraic logic, pure and simple. It is logic in an algebraic dressing.  ...  The first author would like to thank the SSHRC of Canada for its financial support while this research was done.  ... 
doi:10.1016/b978-0-444-51621-3.50010-4 fatcat:xlm77neeubhl7omhhrxhdtuo4q
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