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Solving satisfiability in fuzzy logics with evolution strategies

Tim Brys, Yann-Michael De Hauwere, Martine De Cock, Ann Nowe
2012 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS)  
Satisfiability in propositional logic is well researched and many approaches to checking and solving exist.  ...  In infinitevalued or fuzzy logics, however, there have only recently been attempts at developing methods for solving satisfiability.  ...  Schockaert et al. conversely propose a solver in [11] which reduces the infinite-valued logic to a finite-valued one and then applies a constraint satisfaction solver to check satisfiability.  ... 
doi:10.1109/nafips.2012.6290998 fatcat:rgoylhh4v5bzraiknq5ocem6ni

New complexity results for Łukasiewicz logic

Miquel Bofill, Felip Manyà, Amanda Vidal, Mateu Villaret
2018 Soft Computing - A Fusion of Foundations, Methodologies and Applications  
One aspect that has been poorly studied in multiple-valued logics, and in particular in Łukasiewicz logic, is the generation of instances of varying difficulty for evaluating, comparing and improving satisfiability  ...  We also define an efficient satisfiability preserving translation of Łukasiewicz logic formulas into Ł-clausal forms.  ...  distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in  ... 
doi:10.1007/s00500-018-3365-9 fatcat:72xjuqrqvffaboqtqjoo3wkspe

On the Failure of the Finite Model Property in some Fuzzy Description Logics [article]

Fernando Bobillo and Felix Bou and Umberto Straccia
2010 arXiv   pre-print
words, finite satisfiability and witnessed satisfiability are different for arbitrary knowledge bases.  ...  In this paper we show that if we allow arbitrary knowledge bases, then the fuzzy DLs ALC under Lukasiewicz and Product fuzzy logics do not verify the FMP even if we restrict to witnessed models; in other  ...  As we will see, in the case of Lukasiewicz this situation does not happen if we consider only unfoldable KBs. A TBox T is acyclic iff it verifies the following three constraints: 1.  ... 
arXiv:1003.1588v1 fatcat:m2cnw3wpkzfu5foxatpyv6wavm

Fuzzy Maximum Satisfiability [article]

Mohamed El Halaby, Areeg Abdalla
2016 arXiv   pre-print
In this paper, we extend the Maximum Satisfiability (MaxSAT) problem to Łukasiewicz logic.  ...  Three possible solutions (encodings) are proposed to the new problem: (1) Disjunctive Linear Relations (DLRs), (2) Mixed Integer Linear Programming (MILP) and (3) Weighted Constraint Satisfaction Problem  ...  Solving satisfiability in fuzzy logics is still growing in theory as well as in application. In addition, to the best of our knowledge, MaxSAT has not been defined over fuzzy logic.  ... 
arXiv:1602.02211v1 fatcat:una3l47hancfxm3kjl5ntemyia

Finite Satisfiability in Infinite-Valued Łukasiewicz Logic [chapter]

Steven Schockaert, Jeroen Janssen, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science  
Although it is well-known that every satisfiable formula in Lukasiewicz' infinite-valued logic L∞ can be satisfied in some finitevalued logic, practical methods for finding an appropriate number of truth  ...  As a first step towards efficient reasoning in L∞, we propose a method to find a tight upper bound on this number which, in practice, often significantly improves the worst-case upper bound of Aguzzoli  ...  Acknowledgments Steven Schockaert was funded as a postdoctoral fellow of the Research Foundation -Flanders. Jeroen Janssen was funded by a joint Research Foundation  ... 
doi:10.1007/978-3-642-04388-8_19 fatcat:3eeh7fqwajga3idy7ojorqk7wq

Preference-based Inconsistency-Tolerant Query Answering under Existential Rules

Marco Calautti, Sergio Greco, Cristian Molinaro, Irina Trubitsyna
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning  
In general, there can be several repairs, so it is often natural and desirable to express preferences among them.  ...  In this paper, we propose a framework for querying inconsistent knowledge bases under user preferences for existential rule languages.  ...  For any language L ⊥ considered here, if RE-PAIR CHECKING and SATISFACTION for L ⊥ are in C in the combined complexity, then PREFERRED REPAIR CHECKING for L ⊥ is in C in the combined complexity if C is  ... 
doi:10.24963/kr.2020/21 dblp:conf/kr/CalauttiGMT20 fatcat:q6pjo5rkbnbvtolkneia4rdbhm

On the Semantic Relationship between Probabilistic Soft Logic and Markov Logic [article]

Joohyung Lee, Yi Wang
2016 arXiv   pre-print
Markov Logic Networks (MLN) and Probabilistic Soft Logic (PSL) are widely applied formalisms in Statistical Relational Learning, an emerging area in Artificial Intelligence that is concerned with combining  ...  This is facilitated by first extending fuzzy logic to allow weights, which can be also viewed as a generalization of PSL, and then relate that generalization to MLN.  ...  Notice that 1 − υ I (F ) represents the distance to satisfaction in the general case. It is 0 when I satisfies F , and becomes bigger as υ I (F ) gets farther from 1.  ... 
arXiv:1606.08896v1 fatcat:e2cfanjipraydkacie62ifcz4a

Ontology-Mediated Query Answering over Log-Linear Probabilistic Data

Stefan Borgwardt, İsmail İlkan Ceylan, Thomas Lukasiewicz
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Their knowledge is inherently uncertain, and hence they are often materialized as probabilistic databases.  ...  as a finite interpretation.  ...  A sentence Φ is satisfied by an interpretation, if I ⊧ Φ, where ⊧ is the standard firstorder satisfaction relation.  ... 
doi:10.1609/aaai.v33i01.33012711 fatcat:epzrqmxrhbarhnx2pp6wlk65m4

A graded BDI agent model to represent and reason about preferences

Ana Casali, Lluís Godo, Carles Sierra
2011 Artificial Intelligence  
In this research note, we introduce a graded BDI agent development framework, g-BDI for short, that allows to build agents as multi-context systems that reason about three fundamental and graded mental  ...  We propose a sound and complete logical framework for them and some logical extensions to accommodate slightly different views on desires.  ...  Moreover, using Łukasiewicz logic one can express the governing axioms of probability theory as logical axioms involving modal formulae of the kind Bϕ.  ... 
doi:10.1016/j.artint.2010.12.006 fatcat:ybyqquaj2vcwvksavncbfd7yo4

Fuzzy description logics with general t-norms and datatypes

Fernando Bobillo, Umberto Straccia
2009 Fuzzy sets and systems (Print)  
In this work we face two problems: the common restriction to Zadeh and Łukasiewicz fuzzy logics and the inability to deal with datatypes different from fuzzy sets.  ...  For instance, classical logic, Zadeh's fuzzy logic, and Łukasiewicz connectives, are bMILP-representable, while Gödel negation is not.  ...  Note also that extending Product logic with Łukasiewicz involutive negation leads to the logic Ł 8 [15] since: • As shown in [12] , Łukasiewicz t-conorm can be defined from Łukasiewicz negation d, Product  ... 
doi:10.1016/j.fss.2009.03.006 fatcat:5pqa2kybp5fzbanrnqspfmjy5e

A Fuzzy Description Logic with Product T-norm

Fernando Bobillo, Umberto Straccia
2007 IEEE International Fuzzy Systems conference proceedings  
Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts.  ...  However, up to date the study of fuzzy DLs has been restricted to the Łukasiewicz logic and the "Zadeh semantics".  ...  Similar to crisp DLs, our tableaux algorithm checks the satisfiability of a fuzzy KB by trying to build a fuzzy tableau, from which it is immediate either to build a model in case KB is satisfiable or  ... 
doi:10.1109/fuzzy.2007.4295443 dblp:conf/fuzzIEEE/BobilloS07 fatcat:qds6hilwofcyxmam27sw5zzpma

Page 4095 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
., Surya Mantha and Toshiro Wakayama, A logical reconstruction of constraint relaxation hier- archies in logic programming (362-374); A. Giordana, L. Saitta and C.  ...  4095 in finitely-valued logics (49-58); Laura Giordano, Defining vari- ants of default logic: a modal approach (59-68); Li-Yen Shue and Reza Zamani, An admissible heuristic search algorithm (69- 75); Lin  ... 

Explanations for Negative Query Answers under Existential Rules

İsmail İlkan Ceylan, Thomas Lukasiewicz, Enrico Malizia, Cristian Molinaro, Andrius Vaicenavičius
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning  
Indeed, explanations have a long history in knowledge representation, and have also been investigated for ontology languages based on description logics and existential rules.  ...  In this paper, we continue this line of research and address another important problem, namely, explaining why a query is not entailed under existential rules, i.e., explaining negative query answers.  ...  In a fixed program, there are the rules to check the satisfiability of the formulas.  ... 
doi:10.24963/kr.2020/23 dblp:conf/kr/CeylanLMMV20 fatcat:rtjlsqsp2jcnnejfxzmsrmzja4

Many-valued logics [chapter]

Erich Peter Klement, Radko Mesiar, Endre Pap
2000 Trends in Logic  
(Siegfried Gottwald). 1 We prefer to use the word interpretation in general and to restrict the use of the word model to particular interpretations which are tied in a specific way with sets of well formed  ...  Besides this logical approach also a more algebraic approach is discussed.  ...  The checking of well formed formulas of any propositional system of manyvalued logic for being logically valid can be done in the same way as for classical logic by determining complete truth degree tables  ... 
doi:10.1007/978-94-015-9540-7_11 fatcat:zzdkno6gxfam3i2b66quaac5ni

Fuzzy Ontology Representation using OWL 2 [article]

Fernando Bobillo, Umberto Straccia
2010 arXiv   pre-print
The need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information.  ...  In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies  ...  the buyer and the seller is determined by the maximal degree of satisfiability of the conjunction Buy Sell under Lukasiewicz fuzzy logic.  ... 
arXiv:1009.3391v3 fatcat:jkpwtim5pvhtzh76hj5pu5kvdu
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