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Stable Models of Fuzzy Propositional Formulas
[chapter]
2014
Lecture Notes in Computer Science
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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]
2016
arXiv
pre-print
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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
2015
Fuzzy sets and systems (Print)
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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
2014
Fuzzy sets and systems (Print)
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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
2008
2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology
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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
2015
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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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]
2011
Lecture Notes in Computer Science
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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
2017
Proceedings of the 9th International Joint Conference on Computational Intelligence
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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]
2009
Lecture Notes in Computer Science
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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
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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
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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
2017
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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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
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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
2020
Mathematics
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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]
2018
arXiv
pre-print
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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
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