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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  ...  On the other hand, it was shown in [14] that for every set of formulas Θ that are satisfiable in infinite-valued Lukasiewicz logic (L ∞ ), there exists a finite number k such that Θ is satisfiable in  ... 
doi:10.1007/978-3-642-04388-8_19 fatcat:3eeh7fqwajga3idy7ojorqk7wq

Łukasiewicz Games

Enrico Marchioni, Michael Wooldridge
2015 ACM Transactions on Computational Logic  
In particular, we present a logical characterisation of the existence of Nash equilibria in finite and infinite Łukasiewicz games.  ...  In this article, we introduce Łukasiewicz games, which overcome this limitation by allowing goals to be specified using Łukasiewicz logics.  ...  We call a Łukasiewicz game on a finite-valued Łukasiewicz logic a finite Łukasiewicz game. A Łukasiewicz game on an infinite Łukasiewicz logic is called an infinite Łukasiewicz game.  ... 
doi:10.1145/2783436 fatcat:tdgcdwy3mfauridrdfvt55wjfe

The Complexity of 3-Valued Łukasiewicz Rules [chapter]

Miquel Bofill, Felip Manyà, Amanda Vidal, Mateu Villaret
2015 Lecture Notes in Computer Science  
In this paper we formally prove that the satisfiability problem for 3-valued Łukasiewicz rules is NP-complete.  ...  It is know that determining the satisfiability of n-valued Łukasiewicz rules is NP-complete for n ≥ 4, as well as that it can be solved in time linear in the length of the formula in the Boolean case (  ...  As future work we propose to analyze the complexity of infinitely-valued Łukasiewicz rules, as well as identify -when testing the satisfiability of 3-valued Łukasiewicz rules with a fixed number of variables  ... 
doi:10.1007/978-3-319-23240-9_18 fatcat:4vpswidsojfbngy7vrvf6f22ke

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

Finding Hard Instances of Satisfiability in Lukasiewicz Logics

Miquel Bofill, Felip Manya, Amanda Vidal, Mateu Villaret
2015 2015 IEEE International Symposium on Multiple-Valued Logic  
One aspect that has been poorly studied in multiplevalued logics, and in particular in Łukasiewicz logics, is the generation of instances of varying difficulty for evaluating, comparing and improving satisfiability  ...  In this paper we present a new class of clausal forms, called Łukasiewicz (Ł-)clausal forms, motivate their usefulness, study their complexity, and report on an empirical investigation that shows an easy-hard-easy  ...  Through this work, we focus in a particular family of many-valued logics: the finite-valued and infinitely-valued Łukasiewicz logics.  ... 
doi:10.1109/ismvl.2015.10 dblp:conf/ismvl/BofillMVV15 fatcat:nt4fg4qbrzardk67p4hczja4mm

Models for Many-Valued Probabilistic Reasoning

T. Flaminio, F. Montagna
2009 Journal of Logic and Computation  
(n + 1)-valued Lukasiewicz logic [1] : An assessment a : In [10] , Mundici shows that the coherence of rational Lukasiewicz assessments is decidable, and, as regards to the computational complexity  ...  In light of Paris work, in [10] Mundici approaches the infinite-valued semantics for the events, showing that the coherence of an assessment a : {φ1, . . . , φ k } → [0, 1] with respect to [0, 1]-valued  ... 
doi:10.1093/logcom/exp013 fatcat:raitwvababbqvlldai2xtf45hm

On the Logical Formalization of Possibilistic Counterparts of States over n-valued Lukasiewicz Events

T. Flaminio, L. Godo, E. Marchioni
2009 Journal of Logic and Computation  
For reasoning about these representable classes of possibilistic states, we introduce many-valued modal logics based on the Rational Łukasiewicz Logic, that are shown to be complete with respect to corresponding  ...  Two classes of possibilistic states over MV-algebras of functions are characterized in terms of (generalized) Sugeno integrals.  ...  of finitely-valued Łukasiewicz logic.  ... 
doi:10.1093/logcom/exp012 fatcat:5nlqy6dzprexzibtdlwz2hct6u

Implicit definability of truth constants in Łukasiewicz logic [article]

Zuzana Haniková
2018 arXiv   pre-print
in Łukasiewicz logic is obtained.  ...  In the framework of propositional Łukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced  ...  Two logics are juxtaposed in this paper: (infinite-valued) Lukasiewicz logic L and Rational Pavelka logic RPL.  ... 
arXiv:1802.08588v1 fatcat:snscv5neinbibmrrtch4h5a7rm

Compactness of first-order fuzzy logics [article]

Seyed Mohammad Amin Khatami
2019 arXiv   pre-print
However, different degrees of satisfiability in many-valued logics, poses various kind of the compactness in these logics. One of this issues is the compactness of K-satisfiability.  ...  Here, after an overview on the results around the compactness of satisfiability and compactness of K-satisfiability in many-valued logic based on continuous t-norms (basic logic), we extend the results  ...  Assume that K be an infinite subset of [0, 1) and T = {(p i → p j } i≤j,i,j∈ω 2 . As K is infinite, every finite subset T f of T is K-satisfiable.  ... 
arXiv:1905.01441v1 fatcat:4e3ca3xhvzhzvgkdfiq5rqzsrm

Tableaux for Maximum Satisfiability in Łukasiewicz Logic

Chu Min Li, Felip Manya, Amanda Vidal
2020 2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)  
The calculus can be naturally extended to other finitely-valued logics.  ...  We define a tableau calculus for solving the MaxSAT problem of 3-valued Łukasiewicz logic, and prove its soundness and completeness.  ...  That approach can be generalized to other finitely-valued logics arising from a single algebra, and, in particular, to any n-valued Łukasiewicz logic.  ... 
doi:10.1109/ismvl49045.2020.00007 fatcat:gil3dbo64fgxdjkkkdw7eg5moe

Page 481 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
In Section | we give a brief historical sketch of the origins of Lukasiewicz many-valued logics and Lukasiewicz algebras.  ...  Then it is proved that none of the sets S,, r finite or infinite, is in the range of T.  ... 

Infinite-Valued Lukasiewicz Logic Based on Principal Lattice Filters

Félix Bou
2010 2010 40th IEEE International Symposium on Multiple-Valued Logic  
This generalizes the approach considered in the infinite-valued Łukasiewicz logic, where the fixed number is the maximum. 40th IEEE International Symposium on Multiple-Valued Logic 0195-623X/10 $26.00  ...  In this paper we axiomatize the formulas that, in the infinite-valued (standard) Łukasiewicz algebra, always take a value above certain fixed number.  ...  Table I CALCULUS I FOR INFINITE-VALUED ŁUKASIEWICZ LOGIC Ł by the calculus in Table I.  ... 
doi:10.1109/ismvl.2010.23 dblp:conf/ismvl/Bou10 fatcat:s2bhwgwe2zhzfnzfnq7jnv2y5m

Games for the Strategic Influence of Expectations

Lluís Godo, Enrico Marchioni
2014 Electronic Proceedings in Theoretical Computer Science  
We offer a logical representation of these games as well as a computational study of the existence of equilibria.  ...  We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own.  ...  Also, we plan to investigate games based on infinite-valued Łukasiewicz logic [2] where players have infinite strategy spaces.  ... 
doi:10.4204/eptcs.146.2 fatcat:vuxyjxib65baxi25kqcs6uls6u

Page 5721 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
finite-valued Lukasiewicz logics.  ...  of infinite-valued logics.  ... 

Page 5358 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
Ca- ractére universel de la construction Y des algébres de Lukasiewicz trivalentes [Representation of a three-valued Lukasiewicz algebra by a three-valued Lukasiewicz algebra of sets.  ...  des algébres de Boole libres dans les algébres 06 ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES 5358 de Lukasiewicz trivalentes libres [Construction of free Boolean al- gebras in free three-valued Lukasiewicz  ... 
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