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Finite Satisfiability in Infinite-Valued Łukasiewicz Logic
[chapter]

2009
*
Lecture Notes in Computer Science
*

Although it is well-known that every

doi:10.1007/978-3-642-04388-8_19
fatcat:3eeh7fqwajga3idy7ojorqk7wq
*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*...##
###
Łukasiewicz Games

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. ...

##
###
The Complexity of 3-Valued Łukasiewicz Rules
[chapter]

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 ...

##
###
New complexity results for Łukasiewicz logic

2018
*
Soft Computing - A Fusion of Foundations, Methodologies and Applications
*

One aspect that has been poorly studied

doi:10.1007/s00500-018-3365-9
fatcat:72xjuqrqvffaboqtqjoo3wkspe
*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*...##
###
Finding Hard Instances of Satisfiability in Lukasiewicz Logics

2015
*
2015 IEEE International Symposium on Multiple-Valued Logic
*

One aspect that has been poorly studied

doi:10.1109/ismvl.2015.10
dblp:conf/ismvl/BofillMVV15
fatcat:nt4fg4qbrzardk67p4hczja4mm
*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*. ...##
###
Models for Many-Valued Probabilistic Reasoning

2009
*
Journal of Logic and Computation
*

(n + 1)-

doi:10.1093/logcom/exp013
fatcat:raitwvababbqvlldai2xtf45hm
*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*...##
###
On the Logical Formalization of Possibilistic Counterparts of States over n-valued Lukasiewicz Events

2009
*
Journal of Logic and Computation
*

For reasoning about these representable classes of possibilistic states, we introduce many-

doi:10.1093/logcom/exp012
fatcat:5nlqy6dzprexzibtdlwz2hct6u
*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*. ...##
###
Implicit definability of truth constants in Łukasiewicz logic
[article]

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. ...

##
###
Compactness of first-order fuzzy logics
[article]

2019
*
arXiv
*
pre-print

However, different degrees of

arXiv:1905.01441v1
fatcat:4e3ca3xhvzhzvgkdfiq5rqzsrm
*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*. ...##
###
Tableaux for Maximum Satisfiability in Łukasiewicz Logic

2020
*
2020 IEEE 50th International Symposium on Multiple-Valued Logic (ISMVL)
*

The calculus can be naturally extended to other

doi:10.1109/ismvl49045.2020.00007
fatcat:gil3dbo64fgxdjkkkdw7eg5moe
*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*. ...##
###
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

2010
*
2010 40th IEEE International Symposium on Multiple-Valued Logic
*

This generalizes the approach considered

doi:10.1109/ismvl.2010.23
dblp:conf/ismvl/Bou10
fatcat:s2bhwgwe2zhzfnzfnq7jnv2y5m
*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. ...##
###
Games for the Strategic Influence of Expectations

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We offer a

doi:10.4204/eptcs.146.2
fatcat:vuxyjxib65baxi25kqcs6uls6u
*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. ...##
###
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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