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Page 4109 of Mathematical Reviews Vol. , Issue 94g
[page]
1994
Mathematical Reviews
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“In this paper we develop a sorted version of type theory; we ex-
tend the syntax and semantics of simple type theory by a higher
order sort concept that includes term declarations. ...
{For the entire collection see MR 94f:68008.}
94g:68097 68T15 03B15 03B35 68Q55
Kohlhase, Michael (D-SAAR; Saarbriicken)
Unification in order-sorted type theory. ...
Extending the Resolution Method with Sorts
1993
International Joint Conference on Artificial Intelligence
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In this paper I extend the standard first-order resolution method with special reasoning mechanisms for sorts. Sorts are unary predicates. ...
Sorted unification exploits the sort restrictions of variables with respect to the sort theory. ...
Lemma 6 Sorted unification is undecidable and of unification type infinitary. Lemma 6 is a worst case result. ...
dblp:conf/ijcai/Weidenbach93
fatcat:bepvvgezzbe7dd6ajo7t56oqxa
Page 1117 of Mathematical Reviews Vol. , Issue 96b
[page]
1996
Mathematical Reviews
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The main emphasis is given to first-order (theory) unification, but the paper also contains substantial information on higher-order unification and unification in sort theories. ...
A spe- cial chapter is devoted to higher-order unification, unification in sort theories and constraint solving. ...
Automated Theorem Proving in First-Order Logic Modulo: On the Difference between Type Theory and Set Theory
[chapter]
2000
Lecture Notes in Computer Science
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When it is applied to some first-order presentations of type theory, it simulates exactly higherorder resolution. In this note, we compare how it behaves on type theory and on set theory. ...
Resolution modulo is a first-order theorem proving method that can be applied both to first-order presentations of simple type theory (also called higher-order logic) and to set theory. ...
Resolution modulo in set theory In set theory, there is no rule rewriting terms to terms. Hence, unification in set theory is simply first-order unification. ...
doi:10.1007/3-540-46508-1_1
fatcat:pddj5d3slzbcfbor7f63unxyki
Page 8134 of Mathematical Reviews Vol. , Issue 2000k
[page]
2000
Mathematical Reviews
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the combinatorial maps in the calculus of inductive con- structions (CIC), a variety of type theory well suited for mechaniz- ing mathematics in higher-order logic. ...
In the third section, we mention some unification results for specific equational theories. ...
Unification and Narrowing in Maude 2.4
[chapter]
2009
Lecture Notes in Computer Science
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Unification is supported in Core Maude, the core rewriting engine of Maude, with commands and metalevel functions for order-sorted unification modulo some frequently occurring equational axioms. ...
This paper introduces novel features of Maude 2.4 including support for unification and narrowing. ...
Order-sorted unification is NP-complete in general because Boolean algebra can be encoded as an order-sorted free theory signature and hence satisfiability can be reduced to an order-sorted free theory ...
doi:10.1007/978-3-642-02348-4_27
fatcat:adxberqkxrhnviqr4ce2aflcfy
Equational Cryptographic Reasoning in the Maude-NRL Protocol Analyzer
2007
Electronical Notes in Theoretical Computer Science
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Order-sorted B-unification plays a crucial role; to obtain this functionality we describe a sort propagation algorithm that filters out unsorted B-unifiers provided by the CiME unification tool. ...
In this paper we extend our framework to include theories of the form ∆ B, where B is the theory of associativity and commutativity and ∆ is convergent modulo B. ...
Order-sorted Unification Modulo Equations As the protocol is specified using an order-sorted theory with AC axioms, narrowing requires an order-sorted AC unification procedure. ...
doi:10.1016/j.entcs.2007.02.053
fatcat:76iv5kvvqzesjclji3zrrizqve
Unification in sort theories and its applications
1996
Annals of Mathematics and Artificial Intelligence
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In this language sorted unification in elementary sort theories is of unification type finitary. ...
Abstract In this article I investigate the properties of unification in sort theories. The usual notion of a sort consisting of a sort symbol is extended to a set of sort symbols. ...
A sort theory L is of type:
The Sorted Unification Algorithm
Definition 4.15 (Notions for Sorted Unification) In order to define sorted unification, we have to extend Definition 3.1. ...
doi:10.1007/bf02127750
fatcat:gdyscp3ddvepnokebhmwtqs434
Order-sorted Equational Unification Revisited
2012
Electronical Notes in Theoretical Computer Science
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This paper presents a rule-based algorithm for performing order-sorted E-unification using an unsorted E-unification decision procedure under assumptions about E that are commonly satisfied in practice ...
In many examples of interest, using order-sorted unification over unsorted unification is able to reduce the total number of unifiers considered, and dramatically improve the performance of the Maude-NRL ...
When those subterms are well-typed with the same topmost sort k, substitutions generated by the unsorted unification procedure should be well-typed as well Provided that the sorts of fresh variables in ...
doi:10.1016/j.entcs.2012.11.010
fatcat:uqqx5qefcbccvnbq2i62lwzptm
Unification theory
1989
Journal of symbolic computation
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This article surveys what is presently known in unification theory and records its early history. 20g ...
Unification theory provides the formal framework for investigations into the properties of this operation. ...
theory can be used to solve unification problems in the sorted equational theory. ...
doi:10.1016/s0747-7171(89)80012-4
fatcat:mjwsvawtirdvbc5dxdflp4n2zi
Unification in many-sorted algebras as a device for incremental semantic analysis
1986
Proceedings of the 13th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '86
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During editing, these rules are evaluated using a unification algorithm for many-sorted algebras with semi-lattice ordered subsorts and non-empty equational theories. ...
Since the general problem is not solvable, we have developed an extension of our unification in order to be able to handle arbitrary equational theories, which works correct with The basic idea is as follows ...
Nons y n t a c t i c a t t r i b u t e f l o w in languagebased e d i t o r s . Proc. 9th ACH symposium on p r i n c i p l e s of programming languages, 1982, pp,196-205 Habermann, N. et ...
doi:10.1145/512644.512665
dblp:conf/popl/SneltingH86
fatcat:vxvbiqhzevhbvf75nehbn2se6e
Special issue on automated deduction: Decidability, complexity, tractability
2010
Journal of symbolic computation
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The main result in this paper is a characterization of a decidable fragment of many-sorted first-order logics important in applications. ...
In the paper Decidable Fragments of Many-Sorted Logic, Aharon Abadi, Alexander Rabinovich and Mooly Sagiv, study a decidable fragment of many-sorted first-order logic that allows the expression of a large ...
doi:10.1016/j.jsc.2009.05.006
fatcat:ojjvruw2jza6tpamkmmgyfk3cq
A Typed Hybrid Description Logic Programming Language with Polymorphic Order-Sorted DL-Typed Unification for Semantic Web Type Systems
2007
arXiv
pre-print
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term typing of LP rules based on a polymorphic, order-sorted, hybrid DL-typed unification as procedural semantics of hybrid DLPs. ...
In this paper we elaborate on a specific application in the context of hybrid description logic programs (hybrid DLPs), namely description logic Semantic Web type systems (DL-types) which are used for ...
The order-sorted unification yields the term of the two sorts (types) in the given sort hierarchy. ...
arXiv:cs/0610006v2
fatcat:szfxxjpbvzej5jq6mjgbrgnmka
Page 2967 of Mathematical Reviews Vol. , Issue 99e
[page]
1999
Mathematical Reviews
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In or- der to prove decidability of unification in the extensions, a class of Horn clause sets called sorted shallow equational theories is in- troduced. ...
We show that saturation under sorted superposi- tion is effective on sorted shallow equational theories. ...
Many-Sorted Unification
[chapter]
1987
A Many-Sorted Calculus Based on Resolution and Paramodulation
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Many-sorted unification is considered; that is, unification in the many-sorted free algebras of terms, where variables, as well as the domains and ranges of functions, are restricted to certain subsets ...
An algorithm for many-sorted unification is given. ...
This paper is concerned with unification in many-sorted empty equational theories. ...
doi:10.1016/b978-0-273-08718-2.50012-2
fatcat:bbah2qnfvzbahid7x456s6mjpy
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