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Multi-adjoint algebras versus non-commutative residuated structures

2015
*
International Journal of Approximate Reasoning
*

Furthermore, a comparison between

doi:10.1016/j.ijar.2015.08.003
fatcat:q27ko7up75an7g3fjnxn4oogfi
*adjoint**negations*and the*negations*introduced in extended-order algebras is presented. ...*Adjoint*triples are an interesting generalization of t-norms and their*residuated*implications, since they increase the flexibility in the framework where they are used. ... . ⊓ ⊔ As a consequence,*adjoint**negations*defined from multi-*adjoint*algebras are*more*general*than*the ones given from symmetrical algebras. ...##
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Algebraic Structure of Adjoint Triples Generating a Weak Negation on the Unit Interval
[chapter]

2020
*
Lecture Notes in Computer Science
*

*Adjoint*

*negations*are a generalization of

*residuated*

*negations*built from the implications of an

*adjoint*triple. ... Specifically, this work shows how to build

*adjoint*triples on the unit interval such that their

*adjoint*

*negations*coincide with a given weak

*negation*. ... The following result, which was proven in [14] , shows that

*adjoint*

*negations*are

*more*general

*than*weak

*negations*. Theorem 1 [14] . ...

##
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On the measure of incoherent information in extended multi-adjoint logic programs

2013
*
2013 IEEE Symposium on Foundations of Computational Intelligence (FOCI)
*

In this paper we continue analyzing the introduction of

doi:10.1109/foci.2013.6602452
dblp:conf/foci/MadridO13
fatcat:jaflixrgojd25iftli2byl2vzy
*negation*into the framework of*residuated*logic programming [8], [10] ; specifically, we focus on extended programs, that is we consider programs ... with strong*negation*. ... However, the pair (p, ∼p) seems to be*more*incoherent w.r.t. I 2*than*w.r.t. I 1 since I 2 makes the pair (p, ∼p) to break the coherence condition to a "bigger degree"*than*I 1 . ...##
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Residuation in non-associative MV-algebras
[article]

2018
*
arXiv
*
pre-print

It is well known that every MV-algebra can be converted into a

arXiv:1810.02405v1
fatcat:rizpjdxt75altmw3tfe4fdm6xq
*residuated*lattice satisfying divisibility and the double*negation*law. ... Further, we study a bit*more*stronger version of an algebra where the binary operation is even monotonous. ... Next we introduce a concept which is weaker*than*that of a*residuated*poset. Namely,*adjointness*will be replaced by the conditions occurring in Lemmata 4 and 5. ...##
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On an Open Problem of U. Höhle - A Characterization of Conditionally Cancellative T-Subnorms
[chapter]

2010
*
Communications in Computer and Information Science
*

Further, we give an equivalence condition for a conditionally cancellativite t-subnorm to be a t-norm and hence show that conditionally cancellativite t-subnorms whose natural

doi:10.1007/978-3-642-14055-6_71
fatcat:yrd6olmuanewpd7outynb3mxpm
*negations*are strong are, ... Its natural*negation*n M is given by n M (x) = sup{t ∈ [0, 1] | M (x, t) = 0}, x ∈ [0, 1] . (4) Note that though n M (0) = 1, it need not be a fuzzy*negation*, since n M (1) can be greater*than*0. ... Thus the*adjoint*pair (I, M ) satisfies (1). Example 1. ...##
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Residuated structures derived from commutative idempotent semirings

2019
*
Discussiones Mathematicae - General Algebra and Applications
*

Then the resulting

doi:10.7151/dmgaa.1300
fatcat:pt5i4xubovdizkta2ect5cx24u
*residuated*lattice even satisfies the double*negation*law. ... To a*residuated*lattice L which does not satisfy the double*negation*law there can be assigned a so-called augmented semiring. This can be used for reconstruction of the so-called core C(L) of L. ... Hence the commutative semiring mentioned in Theorem 2.3 is*more*general*than*the MV-semiring from [1] . ...##
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General coupled semirings of residuated lattices

2016
*
Fuzzy sets and systems (Print)
*

We generalize this correspondence to

doi:10.1016/j.fss.2015.12.009
fatcat:lvoigp55dzdypn5hhm2ezx3nla
*residuated*lattices satisfying the double*negation*law. ... In order to prove that L(C) is a*residuated*lattice we have to check the*adjointness*property. ... We will work with*residuated*lattices having one*more*property. Definition 3. Let L = (L, ∨, ∧, ⊗, →, 0, 1) be a*residuated*lattice. ...##
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Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations

2019
*
Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
*

Fuzzy relation equations have recently been extended to a

doi:10.2991/eusflat-19.2019.81
dblp:conf/eusflat/LoboPM19
fatcat:xmn7czajqfh3rc3ds77ep257ky
*more*general framework in which the unknown variables appear together with their logical*negation*connectives, giving rise to the called bipolar ... This paper shows an abductive procedure for a special kind of normal*residuated*logic program by means of bipolar maxproduct fuzzy relation equations. ... It is convenient to mention that there might be*more**than*one possibility for these inputs. ...##
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Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

2020
*
Mathematics
*

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-

doi:10.3390/math8060881
fatcat:3wr4vsbbfvew5ibekvglpsvrlm
*adjoint*normal logic programming. ... Specifically, it is shown how core fuzzy answer set programs can be translated into multi-*adjoint*normal logic programs and vice versa, preserving the semantics of the starting program. ...*adjoint*pairs and a*negation*operator. ...##
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Towards a Fuzzy Answer Set Semantics for Residuated Logic Programs

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

doi:10.1109/wiiat.2008.357
dblp:conf/iat/MadridO08
fatcat:4a4g7hdpuzeerc5l5agj6six54
*residuated*logic programs with*negation*. ... Definition 2 A*residuated*lattice with*negation*is an algebra (L, * , ←, ∼, ¬), where (L, * , ←) is a*residuated*lattice, ∼ is a*negation*operator and ¬ is a default*negation*operator. ... In this paper, we focus on the initial definitions of stable model and answer set in the framework of*residuated*logic programs [2] , as a initial step towards an answer set semantics for multi-*adjoint*...##
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Duality vs. adjunction for fuzzy mathematical morphology and general form of fuzzy erosions and dilations

2009
*
Fuzzy sets and systems (Print)
*

A pair of operators (I, C) are said

doi:10.1016/j.fss.2009.01.006
fatcat:uuzjbg7apnfo3nxc6t666vktom
*adjoint*if: ∀( , , ) ∈ [0, 1] 3 , C( , ) ⇔ I ( , ). (3) The*adjoint*of a conjunction is a*residual*implication (there is an equivalence between the*residuation*principle ... The*negation*writes c( ) = (1 − p ) 1/ p , the t-norm T ( , ) = max(0, ( p + p − 1) 1/ p ), the dual t-cornom S( , ) = min(1, ( p + p ) 1/ p ) and the*residual*implication I ( , ) = min(1, ((1 − ) p + ...##
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Dual multi-adjoint concept lattices

2013
*
Information Sciences
*

of the multi-

doi:10.1016/j.ins.2012.10.030
fatcat:z72hqglbgjgzlai6tsttakdywm
*adjoint*paradigm is applied and no*negation*on the lattices is needed. ... Whereas the usual approach to the latter is via a*negation*operator, this paper presents a fuzzy generalization of the dual concept lattice, the dual multi-*adjoint*concept lattice, in which the philosophy ... of inaccurate) information, which will give*more*flexibility*than*the existing procedures. ...##
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On Coherence and Consistence in Fuzzy Answer Set Semantics for Residuated Logic Programs
[chapter]

2009
*
Lecture Notes in Computer Science
*

In this work we recall the first steps towards the definition of an answer set semantics for

doi:10.1007/978-3-642-02282-1_8
fatcat:hgrbkqsep5e4re4irh2op4jbmu
*residuated*logic programs with*negation*, and concentrate on the development of relationships between the notions ... The previous example presented some*negations*which grant*more*or less restrictive consistence values; however, one would like to be able to construct the corresponding*negation*to a prescribed consistence ... Then we initiate the analysis of the relationships between the notions of coherence of an interpretation with the*more*common notion of consistence. 2 On fuzzy answer set semantics for*residuated*programs ...##
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POSITIVE LOGIC WITH ADJOINT MODALITIES: PROOF THEORY, SEMANTICS, AND REASONING ABOUT INFORMATION

2010
*
The Review of Symbolic Logic
*

Despite absence of

doi:10.1017/s1755020310000134
fatcat:byi5bppldzeebnbe3i6cro5yzi
*negation*and implication, and of axioms corresponding to the characteristic axioms of (e.g.) ... For such a logic we present an algebraic semantics, using lattices with agent-indexed families of*adjoint*pairs of operators, and a cut-free sequent calculus. ... For example, in category Sup of sup-lattices with join-preserving maps, every such map is*residuated*, i.e. has a right*adjoint*. ...##
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Positive Logic with Adjoint Modalities: Proof Theory, Semantics and Reasoning about Information

2009
*
Electronical Notes in Theoretical Computer Science
*

Despite absence of

doi:10.1016/j.entcs.2009.07.102
fatcat:huz6cihturbubjjfhwpfx3sqsi
*negation*and implication, and of axioms corresponding to the characteristic axioms of (e.g.) ... For such a logic we present an algebraic semantics, using lattices with agent-indexed families of*adjoint*pairs of operators, and a cut-free sequent calculus. ... For example, in category Sup of sup-lattices with join-preserving maps, every such map is*residuated*, i.e. has a right*adjoint*. ...
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