Filters








2,342 Hits in 3.5 sec

Stable Models of Fuzzy Propositional Formulas [chapter]

Joohyung Lee, Yi Wang
2014 Lecture Notes in Computer Science  
We introduce the stable model semantics for fuzzy propositional formulas, which generalizes both fuzzy propositional logic and the stable model semantics of Boolean propositional formulas.  ...  We show that several properties of Boolean stable models are naturally extended to this formalism, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics  ...  This work was partially supported by the National Science Foundation under Grant IIS-1319794 and by the South Korea IT R&D program MKE/KIAT 2010-TD-300404-001.  ... 
doi:10.1007/978-3-319-11558-0_23 fatcat:6yjumgnot5fyxjlrhjhv5lipqq

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

Joohyung Lee, Yi Wang
2016 arXiv   pre-print
Despite their resemblance, the relationship has not been formally stated. In this paper, we describe the precise semantic relationship between them from a logical perspective.  ...  We observe that the relationship between PSL and MLN is analogous to the known relationship between fuzzy logic and Boolean logic, and furthermore the weight scheme of PSL is essentially a generalization  ...  This work was partially supported by the National Science Foundation under Grants IIS-1319794, IIS-1526301, and a gift funding from Robert Bosch LLC.  ... 
arXiv:1606.08896v1 fatcat:e2cfanjipraydkacie62ifcz4a

On the relationship between fuzzy autoepistemic logic and fuzzy modal logics of belief

Marjon Blondeel, Tommaso Flaminio, Steven Schockaert, Lluís Godo, Martine De Cock
2015 Fuzzy sets and systems (Print)  
Fuzzy autoepistemic logic is a generalization of autoepistemic logic that allows to represent an agent's rational beliefs on gradable propositions.  ...  Finally, we generalize Levesque's results on stable expansions, belief sets, and "only knowing" operators to our setting, and provide a complete axiomatization for a logic of "only knowing" in the Ł c  ...  Acknowledgements The authors are grateful to anonymous reviewers for their helpful comments and suggestions that have helped to improve the final presentation of this paper.  ... 
doi:10.1016/j.fss.2015.02.018 fatcat:tedcqm4f6rd2fepmzkgby4pbva

Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2014 Fuzzy sets and systems (Print)  
It extends propositional logic by offering the ability to reason about an agent's (lack of) beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming.  ...  We show that many properties from classical autoepistemic logic, e.g. the equivalence between autoepistemic models and stable expansions, remain valid under this generalization.  ...  To prove Proposition 4 we will use the result from Propostion 5. Proposition 5. Every set of objective formulas in L B has a unique fuzzy stable expansion.  ... 
doi:10.1016/j.fss.2012.09.012 fatcat:mfbvgiydovesrpruo2v5xn3avu

Towards a Fuzzy Answer Set Semantics for Residuated Logic Programs

Nicolás Madrid, Manuel Ojeda-Aciego
2008 2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology  
In this work we introduce the first steps towards the definition of an answer set semantics for residuated logic programs with negation.  ...  Hereafter, specially in a semantic context, we will use the term stable model to refer to a stable set.  ...  To begin with, in the following proposition, we state the relationship between the concepts of fuzzy answer sets for a normal program and stable model for a definite program.  ... 
doi:10.1109/wiiat.2008.357 dblp:conf/iat/MadridO08 fatcat:4a4g7hdpuzeerc5l5agj6six54

Handling Uncertainty in Answer Set Programming

Yi Wang, Joohyung Lee
2015 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We present a probabilistic extension of logic programs under the stable model semantics, inspired by the concept of Markov Logic Networks.  ...  The proposed language takes advantage of both formalisms in a single framework, allowing us to represent commonsense reasoning problems that require both logical and probabilistic reasoning in an intuitive  ...  In our previous work (Lee and Wang 2014) , we proposed a stable model semantics for fuzzy propositional formulas, which properly generalizes both fuzzy logic and the Boolean stable model semantics, as  ... 
doi:10.1609/aaai.v29i1.9726 fatcat:martcg4kprgonkuwac5dtobqcq

Fuzzy Autoepistemic Logic: Reflecting about Knowledge of Truth Degrees [chapter]

Marjon Blondeel, Steven Schockaert, Martine De Cock, Dirk Vermeir
2011 Lecture Notes in Computer Science  
Moreover, it is well known to generalize the stable model semantics of answer set programming.  ...  Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity with which a property is satisfied.  ...  The set Th(S) contains all formulas that are true in every interpretation in S. The following proposition describes the relation between stable expansions and autoepistemic models.  ... 
doi:10.1007/978-3-642-22152-1_52 fatcat:kc3crepsknerpm4fienzuxhmne

Solving Fuzzy Answer Set Programs in Product Logic

Ivor Uhliarik
2017 Proceedings of the 9th International Joint Conference on Computational Intelligence  
modeling partial truth (fuzzy logic).  ...  Moreover, there has been no research focused on the product logic semantics in FASP.  ...  ACKNOWLEDGEMENTS The research reported in this paper was supported by the grant UK/367/2017.  ... 
doi:10.5220/0006518303670372 dblp:conf/ijcci/Uhliarik17 fatcat:h5soko66cnhcxeupg6g4sro75q

On Coherence and Consistence in Fuzzy Answer Set Semantics for Residuated Logic Programs [chapter]

Nicolás Madrid, Manuel Ojeda-Aciego
2009 Lecture Notes in Computer Science  
In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions  ...  It is convenient to note that stable models, from which the answer set semantics arose, were initially aimed at formalizing the use of negation in logic programming as negation-as-failure and, thus, are  ...  Corollary 1 . 1 If M is a fuzzy coherent model of P, then any other model T such that T ≤ M is a coherent model.  ... 
doi:10.1007/978-3-642-02282-1_8 fatcat:hgrbkqsep5e4re4irh2op4jbmu

Page 7307 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
syntactical relation of equivalence of tableaux which is a finer relation than the semantical equivalence of formulas.  ...  Summary: “One of the possible semantics of fuzzy sets is in terms of similarity; namely, a grade of membership of an item in a fuzzy set can be viewed as the degree of resemblance between this item and  ... 

Page 18 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
The axioms in question are those of pseudo-Boolean algebras and predicate formulas expressing that the stable elements (the ones for which —7a=a) form an atomic Boolean algebra, and the operation bt+>{  ...  Propositional formulas of the logic of problems are translated into terms (when propositional connectives are translated into functions).  ... 

Minimal Undefinedness for Fuzzy Answer Sets

Mario Alviano, Giovanni Amendola, Rafael Peñaloza
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Fuzzy Answer Set Programming (FASP) combines the non-monotonic reasoning typical of Answer Set Programming with the capability of Fuzzy Logic to deal with imprecise information and paraconsistent reasoning  ...  Algorithms that minimize undefinedness of fuzzy answer sets are presented, and implemented.  ...  Intuitively, L-stable model semantics selects those 3-valued stable models, where a smallest set of atoms is undefined.  ... 
doi:10.1609/aaai.v31i1.11045 fatcat:dxndywbrvjeqznubpclgzsihn4

Page 2538 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
95e:03055 power to govern a model in the limit: when the “until” modality operator is included, then nesting modalities do constrain the limit of a model more than any nonnested formula.  ...  This modal semantic interpretation enables one to form a union of propositional calculus, probability theory, fuzzy set theory, possi- bility theory, and evidence theory into a joint modal framework.  ... 

Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

M. Eugenia Cornejo, David Lobo, Jesús Medina
2020 Mathematics  
Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer  ...  As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained.  ...  Acknowledgments: The author would like to thank the four anonymous reviewers for their careful reading of the paper and useful suggestions to clarify this work.  ... 
doi:10.3390/math8060881 fatcat:3wr4vsbbfvew5ibekvglpsvrlm

A van Benthem Theorem for Fuzzy Modal Logic [article]

Paul Wild, Lutz Schröder, Dirk Pattinson, Barbara König
2018 arXiv   pre-print
We present a fuzzy (or quantitative) version of the van Benthem theorem, which characterizes propositional modal logic as the bisimulation-invariant fragment of first-order logic.  ...  Specifically, we consider a first-order fuzzy predicate logic along with its modal fragment, and show that the fuzzy first-order formulas that are non-expansive w.r.t. the natural notion of bisimulation  ...  As indicated above, we thus equip the propositional connectives with Zadeh semantics.  ... 
arXiv:1802.00478v2 fatcat:nypcw2p4kvefxefmrpv7vorsp4
« Previous Showing results 1 — 15 out of 2,342 results