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Contraction in propositional logic

Thomas Caridroit, Sébastien Konieczny, Pierre Marquis
2017 International Journal of Approximate Reasoning  
In this paper, we present postulates for the contraction of propositional belief bases which correspond to the AGM postulates for the contraction of belief sets.  ...  In the context of finite propositional logic, Katsuno and Mendelzon pointed out postulates for the revision of belief bases which correspond to the AGM postulates for the revision of beliefs sets.  ...  Conclusion and Perspectives In this paper we investigated belief contraction in the framework of finite propositional logic.  ... 
doi:10.1016/j.ijar.2016.06.010 fatcat:2vpy6nb2yzc47lbmikypy4575y

Contraction in Propositional Logic [chapter]

Thomas Caridroit, Sébastien Konieczny, Pierre Marquis
2015 Lecture Notes in Computer Science  
In this paper, we present postulates for the contraction of propositional belief bases which correspond to the AGM postulates for the contraction of belief sets.  ...  In the context of finite propositional logic, Katsuno and Mendelzon pointed out postulates for the revision of belief bases which correspond to the AGM postulates for the revision of beliefs sets.  ...  Conclusion and Perspectives In this paper we investigated belief contraction in the framework of finite propositional logic.  ... 
doi:10.1007/978-3-319-20807-7_17 fatcat:ykidvckz2vb3jpazlqovtb72ce

Decision Problems for Second-Order Linear Logic [chapter]

P. D. Lincoln, A. Scedrov, N. Shankar
1997 Logic and Scientific Methods  
It is shown that the structural rules of contraction and weakening may be simulated by second-order propositional quanti ers and the multiplicative connectives.  ...  Among the consequences are the undecidability of the intuitionistic second-order fragment of propositional multiplicative linear logic and the undecidability of multiplicative linear logic with rst-order  ...  classical logic In this section we represent second-order classical predicate logic lk12 in mll12 and in mall12.  ... 
doi:10.1007/978-94-017-0487-8_7 fatcat:sp5afdrfa5hythn66hgfja5nkq

Minimal change: Relevance and recovery revisited

Márcio M. Ribeiro, Renata Wassermann, Giorgos Flouris, Grigoris Antoniou
2013 Artificial Intelligence  
Motivated by the fact that non-classical logics (like Description Logics or Horn logic) are increasingly being used in various applications, we study contraction for all monotonic logics, classical or  ...  The operation of contraction (referring to the removal of knowledge from a knowledge base) has been extensively studied in the research field of belief change, and different postulates (e.g., the AGM postulates  ...  Thus, it is enough to contract any one proposition from A, rather than all propositions in A; in the terminology of Fuhrmann [22] , this corresponds to choice contraction (which is more suitable for our  ... 
doi:10.1016/j.artint.2013.06.001 fatcat:67rbbkflrffe3cuxfojkzuwi2y

Contraction-elimination for implicational logics

Ryo Kashima
1997 Annals of Pure and Applied Logic  
BCK-logic), then there is a propositional variable which is PNN (resp. PPN) in A (Corollary 1.3) .  ...  PPN) in the sequent, then it is provable without the right (resp. left) contraction rule, where a propositional variable a is said to be PNN (resp.  ...  this paper, we consider only the implicational fragments of propositional logics (except in the remark (4) in this section).  ... 
doi:10.1016/s0168-0072(97)81394-2 fatcat:gtib7y2dvvespi4ehpdyjwmabq

A Formal Language for Electronic Contracts [chapter]

Cristian Prisacariu, Gerardo Schneider
2007 Lecture Notes in Computer Science  
In this paper we propose a formal language for writing electronic contracts, based on the deontic notions of obligation, permission, and prohibition.  ...  We provide a translation of the contract language into the logic, the semantics of which faithfully captures the meaning of obligation, permission and prohibition.  ...  Proof: The proof is similar to the proposition above. 2 The following proposition expresses that the most important paradoxes of deontic logic are avoided in our contract language, either because there  ... 
doi:10.1007/978-3-540-72952-5_11 fatcat:zhz6hocitvh6ffahxfxt3gjse4

Page 1532 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
(E-SALA-QS; Salamanca) Intuitionistic propositional logic without ‘contraction’ but with ‘reductio’. (English summary) Studia Logica 66 (2000), no. 3, 409-418.  ...  admissible rules of intuitionistic propositional logic.  ... 

A taste of linear logic [chapter]

Philip Wadler
1993 Lecture Notes in Computer Science  
The presentation of linear logic is simpli ed by basing it on the Logic of Unity. An application to the array update problem is brie y discussed.  ...  This tutorial paper provides an introduction to intuitionistic logic and linear logic, and shows how they correspond to type systems for functional languages via the notion of'Propositions as Types'.  ...  If Contraction or Weakening are used in a proof, then this will be explicitly visible in the proposition proved.  ... 
doi:10.1007/3-540-57182-5_12 fatcat:rqrdqjxzkfegdeuvopist55urm

A Generalisation of AGM Contraction and Revision to Fragments of First-Order Logic

Zhiqiang Zhuang, Zhe Wang, Kewen Wang, James Delgrande
2019 The Journal of Artificial Intelligence Research  
AGM contraction and revision assume an underlying logic that contains propositional logic.  ...  We redefine entrenchment-based contraction in ways that apply to any FC logic, which we call FC contraction.  ...  Therefore, when the underlying logic is propositional logic, FC contraction coincides with entrenchment-based contraction. Proposition 2. Let the underlying logic be propositional logic.  ... 
doi:10.1613/jair.1.11337 fatcat:prcimkdh4bgfxihimfftgaj6k4

Page 2877 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
Using basic propositional calculus logic in the sense of A.  ...  into basic propositional logic.  ... 

Contracting Logics [chapter]

Márcio M. Ribeiro, Marcelo E. Coniglio
2012 Lecture Notes in Computer Science  
Besides removing the 'undesirable' rule, this operation (called contraction) should change the logic in a minimal way.  ...  In this paper, inspired in the field of belief revision, it is presented a novel operation for defining a new logic given a known logic.  ...  As an application it was proved that the logics P 1 and I 1 are strongly maximal w.r.t. Classical Propositional Logic. This paper focused in the contraction of one rule from a logic.  ... 
doi:10.1007/978-3-642-32621-9_20 fatcat:cfjuez672jcg7nfw3zttuipvr4

AGM Contraction and Revision of Rules

Guido Boella, Gabriella Pigozzi, Leendert van der Torre
2016 Journal of Logic, Language and Information  
In this paper we study AGM contraction and revision of rules using input/output logical theories.  ...  We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator  ...  Acknowledgments Thanks to David Makinson and Jörg Hansen for discussions on the issues raised in this paper.  ... 
doi:10.1007/s10849-016-9244-9 fatcat:tbxxgvwb7zfv3fobmldpboaa7u

Page 228 of Computational Linguistics Vol. 25, Issue 2 [page]

1999 Computational Linguistics  
Note that if [ + A is provable in the multiplicative intuitionistic noncommutative linear logic, then + (['*)*, A* is provable in the multiplicative noncommutative linear logic, where: e for each formula  ...  Computational Linguistics Volume 25, Number 2 re aéA r,AFA rkKA- rrA,A (1 — weakening) (r — weakening) r,A,AFA ac isialiaiaal rrA,A,A FAFA (l — contraction) TFA.A (r — contraction) PB ATA | hange) Tt Av  ... 

Some Logics of Belief and Disbelief [chapter]

Samir Chopra, Johannes Heidema, Thomas Meyer
2003 Lecture Notes in Computer Science  
In this paper we present four logics of disbelief which address some or all of these intuitions.  ...  The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways.  ...  For example, ÈÄ denotes classical consequence for propositional logic.  ... 
doi:10.1007/978-3-540-24581-0_31 fatcat:zhip46occjg7jkmsvyktjnthja

Page 2265 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
Let I(a@) denote a normal modal logic formed on the base of the intuitionistic propositional logic and having a as specific axiom.  ...  It is shown that revision can be defined as contraction followed by addition, and contraction on a proposition A can be defined as a mixture of what is believed when A is accepted and what would be believed  ... 
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