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Recent Advances in Unification for the EL Family EL家族统一的最新进展
UNIF Pub Date : 2014-07-28 DOI: 10.29007/q5px
F. Baader, Stefan Borgwardt, Barbara Morawska
{"title":"Recent Advances in Unification for the EL Family","authors":"F. Baader, Stefan Borgwardt, Barbara Morawska","doi":"10.29007/q5px","DOIUrl":"https://doi.org/10.29007/q5px","url":null,"abstract":"Unification in Description Logics (DLs) has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the DL EL, which is used to define several large biomedical ontologies, unification is NP-complete. Several algorithms that solve unification in EL have previously been presented. In this paper, we summarize recent extensions of these algorithms that can deal with general concept inclusion axioms (GCIs), role hierarchies (H), and transitive roles (R). For the algorithms to be complete, however, the ontology consisting of the GCIs and role axioms needs to satisfy a certain cycle restriction.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129380593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The use of types in designing unification algorithms: two case studies 在设计统一算法中使用类型:两个案例研究
UNIF Pub Date : 2014-07-28 DOI: 10.29007/lbk5
Serdar Erbatur, Santiago Escobar, P. Narendran
{"title":"The use of types in designing unification algorithms: two case studies","authors":"Serdar Erbatur, Santiago Escobar, P. Narendran","doi":"10.29007/lbk5","DOIUrl":"https://doi.org/10.29007/lbk5","url":null,"abstract":"We discuss the use of type systems in a non-strict sense when designing uni cation algorithms. We rst give a new (rule-based) algorithm for an equational theory which represents a property of El-Gamal signature schemes and show how a type system can be used to prove termination of the algorithm. Lastly, we reproduce a termination result for theory of partial exponentiation given earlier.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126057648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounded Higher-order Unification using Regular Terms 使用正则项的有界高阶统一
UNIF Pub Date : 2014-07-28 DOI: 10.29007/zhpc
Tomer Libal
{"title":"Bounded Higher-order Unification using Regular Terms","authors":"Tomer Libal","doi":"10.29007/zhpc","DOIUrl":"https://doi.org/10.29007/zhpc","url":null,"abstract":"We present a procedure for the bounded unication of higher-order terms [24]. The procedure extends G. P. Huet’s pre-unication procedure [11] with rules for the generation and folding of regular terms. The concise form of the procedure allows the reuse of the pre-unication correctness proof. Furthermore, the regular terms can be restricted in order to get a decidable uniability problem. Finally, the procedure avoids re-computation of terms in a non-deterministic search which leads to a better performance in practice when compared to other bounded unication algorithms.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133222131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Some Notes on Basic Syntactic Mutation 关于基本句法变异的一些注意事项
UNIF Pub Date : 2014-07-28 DOI: 10.29007/sdp1
Kimberly A. Gero, Christopher Bouchard, P. Narendran
{"title":"Some Notes on Basic Syntactic Mutation","authors":"Kimberly A. Gero, Christopher Bouchard, P. Narendran","doi":"10.29007/sdp1","DOIUrl":"https://doi.org/10.29007/sdp1","url":null,"abstract":"Unification modulo convergent term rewrite systems is an important research area with many applications. In their seminal paper Lynch and Morawska gave three conditions on rewrite systems that guarantee that unifiability can be checked in polynomial time (P). We show that these conditions are tight, in the sense that relaxing any one of them will “upset the applecart,” giving rise to unification problems that are not in P (unless P = NP), and in doing so address an open problem posed by Lynch and Morawska. We also investigate a related decision problem: we show the undecidability of subterm-collapse for the restricted term rewriting systems that we are considering.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115949598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Asymmetric Unification: A New Unification Paradigm for Cryptographic Protocol Analysis 非对称统一:密码协议分析的新统一范式
UNIF Pub Date : 2013-06-09 DOI: 10.1007/978-3-642-38574-2_16
Serdar Erbatur, Santiago Escobar, D. Kapur, Zhiqiang Liu, C. Lynch, C. Meadows, J. Meseguer, P. Narendran, Sonia Santiago, R. Sasse
{"title":"Asymmetric Unification: A New Unification Paradigm for Cryptographic Protocol Analysis","authors":"Serdar Erbatur, Santiago Escobar, D. Kapur, Zhiqiang Liu, C. Lynch, C. Meadows, J. Meseguer, P. Narendran, Sonia Santiago, R. Sasse","doi":"10.1007/978-3-642-38574-2_16","DOIUrl":"https://doi.org/10.1007/978-3-642-38574-2_16","url":null,"abstract":"","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"293 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123113677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
On the Complexity of the Tiden-Arnborg Algorithm for Unification modulo One-Sided Distributivity 关于统一模单侧分布的Tiden-Arnborg算法的复杂性
UNIF Pub Date : 2010-12-21 DOI: 10.4204/EPTCS.42.5
P. Narendran, Andrew M. Marshall, B. Mahapatra
{"title":"On the Complexity of the Tiden-Arnborg Algorithm for Unification modulo One-Sided Distributivity","authors":"P. Narendran, Andrew M. Marshall, B. Mahapatra","doi":"10.4204/EPTCS.42.5","DOIUrl":"https://doi.org/10.4204/EPTCS.42.5","url":null,"abstract":"We prove that the Tiden and Arnborg algorithm for equational unification modulo one-sided distributivity is not polynomial time bounded as previously thought. A set of counterexamples is developed that demonstrates that the algorithm goes through exponentially many steps.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"151 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133305888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints 等式约束列表的幂等MGU公理的机器校验模型
UNIF Pub Date : 2010-12-21 DOI: 10.4204/EPTCS.42.3
Sunil Kothari, J. Caldwell
{"title":"A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints","authors":"Sunil Kothari, J. Caldwell","doi":"10.4204/EPTCS.42.3","DOIUrl":"https://doi.org/10.4204/EPTCS.42.3","url":null,"abstract":"We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125640908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Towards Correctness of Program Transformations Through Unification and Critical Pair Computation 从统一和临界对计算探讨程序变换的正确性
UNIF Pub Date : 2010-12-21 DOI: 10.4204/EPTCS.42.4
Conrad Rau, M. Schmidt-Schauß
{"title":"Towards Correctness of Program Transformations Through Unification and Critical Pair Computation","authors":"Conrad Rau, M. Schmidt-Schauß","doi":"10.4204/EPTCS.42.4","DOIUrl":"https://doi.org/10.4204/EPTCS.42.4","url":null,"abstract":"Correctness of program transformations in extended lambda calculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach to proving correctness is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules, and then of so-called complete sets of diagrams. The method is similar to the computation of critical pairs for the completion of term rewriting systems. We explore cases where the computation of these overlaps can be done in a first order way by variants of critical pair computation that use unification algorithms. As a case study we apply the method to a lambda calculus with recursive let-expressions and describe an effective unification algorithm to determine all overlaps of a set of transformations with all reduction rules. The unification algorithm employs many-sorted terms, the equational theory of left-commutativity modelling multi-sets, context variables of different kinds and a mechanism for compactly representing binding chains in recursive let-expressions.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124826436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Unification modulo a partial theory of exponentiation 统一模:指数的部分理论
UNIF Pub Date : 2010-12-21 DOI: 10.4204/EPTCS.42.2
D. Kapur, Andrew M. Marshall, P. Narendran
{"title":"Unification modulo a partial theory of exponentiation","authors":"D. Kapur, Andrew M. Marshall, P. Narendran","doi":"10.4204/EPTCS.42.2","DOIUrl":"https://doi.org/10.4204/EPTCS.42.2","url":null,"abstract":"Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134516744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Nominal Unification Revisited 重新审视名义统一
UNIF Pub Date : 2010-12-21 DOI: 10.4204/EPTCS.42.1
Christian Urban
{"title":"Nominal Unification Revisited","authors":"Christian Urban","doi":"10.4204/EPTCS.42.1","DOIUrl":"https://doi.org/10.4204/EPTCS.42.1","url":null,"abstract":"Nominal unification calculates substitutions that make terms involving binders equal modulo alpha-equivalence. Although nominal unification can be seen as equivalent to Miller's higher-order pattern unification, it has properties, such as the use of first-order terms with names (as opposed to alpha-equivalence classes) and that no new names need to be generated during unification, which set it clearly apart from higher-order pattern unification. The purpose of this paper is to simplify a clunky proof from the original paper on nominal unification and to give an overview over some results about nominal unification.","PeriodicalId":164988,"journal":{"name":"UNIF","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129520037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
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