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Page 4109 of Mathematical Reviews Vol. , Issue 94g
[page]

1994
*
Mathematical Reviews
*

“

*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*. ...##
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Extending the Resolution Method with Sorts

1993
*
International Joint Conference on Artificial Intelligence
*

*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. ...

##
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Page 1117 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

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. ...##
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Automated Theorem Proving in First-Order Logic Modulo: On the Difference between Type Theory and Set Theory
[chapter]

2000
*
Lecture Notes in Computer Science
*

When it is applied to some first-

doi:10.1007/3-540-46508-1_1
fatcat:pddj5d3slzbcfbor7f63unxyki
*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*. ...##
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Page 8134 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

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*. ...##
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Unification and Narrowing in Maude 2.4
[chapter]

2009
*
Lecture Notes in Computer Science
*

*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*...

##
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Equational Cryptographic Reasoning in the Maude-NRL Protocol Analyzer

2007
*
Electronical Notes in Theoretical Computer Science
*

*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. ...

##
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Unification in sort theories and its applications

1996
*
Annals of Mathematics and Artificial Intelligence
*

*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. ...

##
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Order-sorted Equational Unification Revisited

2012
*
Electronical Notes in Theoretical Computer Science
*

This paper presents a rule-based algorithm for performing

doi:10.1016/j.entcs.2012.11.010
fatcat:uqqx5qefcbccvnbq2i62lwzptm
*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*...##
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Unification theory

1989
*
Journal of symbolic computation
*

This article surveys what is presently known

doi:10.1016/s0747-7171(89)80012-4
fatcat:mjwsvawtirdvbc5dxdflp4n2zi
*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*. ...##
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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
*

During editing, these rules are evaluated using a

doi:10.1145/512644.512665
dblp:conf/popl/SneltingH86
fatcat:vxvbiqhzevhbvf75nehbn2se6e
*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 ...##
###
Special issue on automated deduction: Decidability, complexity, tractability

2010
*
Journal of symbolic computation
*

The main result

doi:10.1016/j.jsc.2009.05.006
fatcat:ojjvruw2jza6tpamkmmgyfk3cq
*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 ...##
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A Typed Hybrid Description Logic Programming Language with Polymorphic Order-Sorted DL-Typed Unification for Semantic Web Type Systems

2007
*
arXiv
*
pre-print

term

arXiv:cs/0610006v2
fatcat:szfxxjpbvzej5jq6mjgbrgnmka
*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. ...##
###
Page 2967 of Mathematical Reviews Vol. , Issue 99e
[page]

1999
*
Mathematical Reviews
*

*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*. ...

##
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Many-Sorted Unification
[chapter]

1987
*
A Many-Sorted Calculus Based on Resolution and Paramodulation
*

Many-

doi:10.1016/b978-0-273-08718-2.50012-2
fatcat:bbah2qnfvzbahid7x456s6mjpy
*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*. ...
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