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Grading Adjoint Logic
[article]

2020
*
arXiv
*
pre-print

We give a sequent calculus, natural deduction, and term assignment for

arXiv:2006.08854v1
fatcat:i5qsfbkd7fgmlmobbbhiaxicci
*Graded**Adjoint**Logic*. ... We introduce a new*logic*that combines*Adjoint**Logic*with*Graded*Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. ...*Graded**Adjoint**Logic*is more general than*Graded*Modal*Logic*, because every semiring is a pointed semiring where all operations are defined. ...##
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Multi-adjoint Logic Programming with Continous Semantics
[chapter]

2001
*
Lecture Notes in Computer Science
*

In this paper we apply this idea to introduce multi-

doi:10.1007/3-540-45402-0_26
fatcat:tiabmzne7vg6pnql2bnlv5vxwy
*adjoint**logic*programs as an extension of monotonic*logic*programs. ... Considering different implication operators, such as Lukasiewicz, Gödel or product implication in the same*logic*program, naturally leads to the allowance of several*adjoint*pairs in the lattice of truthvalues ... Syntax of Multi-*Adjoint**Logic*Programs The definition of multi-*adjoint**logic*program is given, as usual, as a set of rules and facts. ...##
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Page 1417 of Mathematical Reviews Vol. , Issue 96c
[page]

1996
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Mathematical Reviews
*

This

*logic*is first-order and is dictated directly by the underlying categorical se- mantics. ... It is a*graded*generalization of a Poisson algebra in which there is a*graded*commutative associative product and (up to suitable signs) a Lie bracket of degree —1 with a signed Leibniz relation between ...##
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A Multi-adjoint Logic Approach to Abductive Reasoning
[chapter]

2001
*
Lecture Notes in Computer Science
*

Multi-

doi:10.1007/3-540-45635-x_26
fatcat:jbzdulh37jbsze7qwyuypjky3y
*adjoint**logic*programs has been recently introduced [9, 10] as a generalization of monotonic*logic*programs [2, 3] , in that simultaneous use of several implications in the rules and rather general ... To model uncertainty in human cognition and real world applications; we use multi-*adjoint**logic*programming to introduce and study a model of abduction problem. ... Syntax and Semantics of Multi-*Adjoint**Logic*Programs Multi-*adjoint**logic*programs are constructed from the abstract syntax induced by a multi-*adjoint*algebra on a set of propositional symbols. ...##
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An algebraic theory of normal forms

1995
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Annals of Pure and Applied Logic
*

. * There is a general theorem by Lawvere of existence of left

doi:10.1016/0168-0072(93)e0084-2
fatcat:cdebx4wvybdu7psf5fzct5kcoy
*adjoints*for algebraic functors which applies to our case. ... One may also directly use some*adjoint*functor theorem (see [17]). 3 This will be our trend for the rest of the paper: we give full details of the general theory and of its applications to the basic example ... for very simple*logics*, like S4). ...##
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A Multi-Adjoint Approach to Similarity-Based Unification

2002
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Electronical Notes in Theoretical Computer Science
*

A formal model for similarity-based fuzzy unification in multi-

doi:10.1016/s1571-0661(04)80515-2
fatcat:lv5stcox2nactnuzuavsxhhqoe
*adjoint**logic*programs is presented. ... computational model, a similarity-based unification approach is constructed by simply adding axioms of fuzzy similarities and using classical crisp unification which provides a semantic framework for*logic*...*logic*programs as follows: Definition 3.5 Let P be a multi-*adjoint**logic*program. ...##
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Page 8070 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
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Mathematical Reviews
*

Propositional calculus under

*adjointness*. (English summary) Possibility theory and fuzzy*logic*. Fuzzy Sets and Systems 132 (2002), no. 1, 91-106. ... We call the resulting*logic*propositional calculus under*adjointness*, abbreviated AdjPC. “Most algebraic theorems on such (L,<), A and K are inequal- ities for the posets (L, <) of truth values. ...##
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Logical Foundations of Quantitative Equality (long version)
[article]

2021
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arXiv
*
pre-print

We introduce a deductive calculus for (

arXiv:2110.05388v1
fatcat:ru46cprs2berzpdcmkyigltmhu
*Graded*) Linear*Logic*with quantitative equality and the notion of Lipschitz doctrine to give semantics to it. ... To overcome this issue, we consider the extension of Linear*Logic*with*graded*modalities and use them to write a resource sensitive substitution rule that keeps equality quantitative. ... n of Bounded Linear*Logic*[23] and, indeed, syntactic doctrines built out from it are N = -*graded*. ...##
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Flat Coalgebraic Fixed Point Logics
[chapter]

2010
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Lecture Notes in Computer Science
*

Extending this notion to the generic semantic framework of coalgebraic

doi:10.1007/978-3-642-15375-4_36
fatcat:j7oactbfsrdp5eogwwtsmepsay
*logic*enables covering a wide range of*logics*beyond the standard mu-calculus including, e.g., flat fragments of the*graded*mu-calculus ... The family of such flat fixpoint*logics*includes, e.g., LTL, CTL, and the*logic*of common knowledge. ...*Graded*fixed point*logics*are sublogics of the*graded*µ-calculus [16] . ...##
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Towards Biresiduated Multi-adjoint Logic Programming
[chapter]

2004
*
Lecture Notes in Computer Science
*

Multi-

doi:10.1007/978-3-540-25945-9_60
fatcat:pc5tqc5fm5ab5ji6c53xkaix4i
*adjoint**logic*programs were recently proposed as a generalization of monotonic and residuated*logic*programs, in that simultaneous use of several implications in the rules and rather general connectives ...*logic*programming and sketch some considerations on its fixpoint semantics. 1. ... As our approach does not require*adjoint*conjunctors to be commutative, it would allow the development of a sound and complete*graded*resolution. 5 (x, y) is not commutative. ...##
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Categorical Accommodation of Graded Fuzzy Topological System, Graded Frame and Fuzzy Topological Space with Graded inclusion
[article]

2017
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arXiv
*
pre-print

The notions of

arXiv:1704.08112v1
fatcat:yn4qovk5urfu3dupjqpiu4o5rm
*graded*fuzzy topological system and fuzzy topological space with*graded*inclusion were obtained via fuzzy geometric*logic*with*graded*con- sequence. ... A detailed study of*graded*frame,*graded*fuzzy topological system and fuzzy topological space with*graded*inclusion is already done in our earlier paper. ... Ext g is the right*adjoint*to the functor J g . Proof. Follows from the combination of the*adjoint*situations in Lemmas 2.7, 4.1. ...##
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Similarity-based unification: a multi-adjoint approach

2004
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Fuzzy sets and systems (Print)
*

The aim of this paper is to build a formal model for similarity-based fuzzy uniÿcation in multi-

doi:10.1016/j.fss.2003.11.005
fatcat:pw3zqhtsavb6pd6xulhckx4l44
*adjoint**logic*programs. ... Speciÿcally, a general framework of*logic*programming which allows the simultaneous use of di erent implications in the rules and rather general connectives in the bodies is introduced, then a procedural ... Let P be a multi-*adjoint**logic*program. ...##
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A Procedural Semantics for Multi-adjoint Logic Programming
[chapter]

2001
*
Lecture Notes in Computer Science
*

Multi-

doi:10.1007/3-540-45329-6_29
fatcat:txt5frgudfgwjb3hyvild4wnwe
*adjoint**logic*program generalise monotonic*logic*programs introduced in [1] in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. ... In this work, a procedural semantics is given for the paradigm of multiadjoint*logic*programming and completeness theorems are proved. ... Definition 2 (Multi-*Adjoint**Logic*Programs). ...##
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An algebraic generalization of Kripke structures

2008
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Mathematical proceedings of the Cambridge Philosophical Society (Print)
*

As additional examples we describe intuitionistic propositional modal

doi:10.1017/s0305004108001667
fatcat:jx5spjwe35a5tibkks7ngipf3a
*logic*, the*logic*of programs PDL, and the ramified temporal*logic*CTL. ... The Kripke semantics of classical propositional normal modal*logic*is made algebraic via an embedding of Kripke structures into the larger class of pointed stably supported quantales. ...*adjoints*. ...##
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Towards Simplification Logic for Graded Attribute Implications with General Semantics

2018
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International Conference on Concept Lattices and their Applications
*

We present variant of simplification

dblp:conf/cla/CorderoE0V18
fatcat:6ezctizxyfdppiejijo2ozw7rq
*logic*for reasoning with if-then dependencies that arise in formal concept analysis of data with*graded*attributes. ... We describe semantics of the rules, axiomatic system of the*logic*, and prove its soundness and completeness. ... The simplification*logic*was later introduced for*graded*attribute implications parameterized by hedges in [4] . ...
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