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A uniform tableaux method for nonmonotonic modal logics [chapter]

Francesco M. Donini, Fabio Massacci, Daniele Nardi, Riccardo Rosati
1996 Lecture Notes in Computer Science  
We present a semantic tableaux calculus for propositional nonmonotonic modal logics, based on possible-worlds characterisations for nonmonotonic modal logics.  ...  This method is parametric with respect to both the modal logic and the preference semantics, since it handles in a uniform way the entailment problem for a wide class of nonmonotonic modal logics: McDermott  ...  We thank the referees for their comments and suggestions for improving the paper.  ... 
doi:10.1007/3-540-61630-6_6 fatcat:icdpv45mxjfwpfndnfix5zz2ta

Sequent-Type Proof Systems for Three-Valued Default Logic [article]

Sopo Pkhakadze
2019 arXiv   pre-print
In my master's thesis, I introduce sequent-type calculi for a variant of default logic employing \Lukasiewicz's three-valued logic as the underlying base logic.  ...  of nonmonotonic reasoning by Bonatti and Olivetti, which employ a complementary calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.  ...  Although Radzikowska [38] gave a resolution-based characterisation of brave reasoning for closed normal default theories, generalising the method for standard default logic as proposed by Reiter [39  ... 
arXiv:1905.04725v1 fatcat:5slb6vgasbhfdfxf5cm64vqhh4

A proof theoretical approach to default reasoning I: tableaux for default logic

G Amati
1996 Journal of Logic and Computation  
The advantage of our approach, besides being simple and neat, is in its generality: it allows for the development of a default theory for any logic with a tableau formulation, such as intuitionistic logic  ...  We present a general proof theoretical methodology for default systems.  ...  Aknowledgments We thank two anonymous referees for accurate suggestions which have improved the paper.  ... 
doi:10.1093/logcom/6.2.205 fatcat:dpbdxncjd5gjjkuazl6ybzw6bm

A Tableau Calculus for Equilibrium Entailment [chapter]

David Pearce, Inmaculada P. de Guzmán, Agustín Valverde
2000 Lecture Notes in Computer Science  
A further tableau calculus is then presented for computing equilibrium entailment. This makes use of a new method for reducing the complexity of the tableau expansion rules, which we call signing-up.  ...  semantics for logic programs.  ...  default and autoepistemic logics; for an overview and additional references for the area, see Olivetti [27] .  ... 
doi:10.1007/10722086_28 fatcat:ph4j6jn7d5ghnno2jjqqjtom6m

Page 3480 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Schwind and Vincent Risch, A tableau-based characterisation for default logic (310-317); Paul Snow, Restraining the proliferation of worlds in probabilistic logic entailments (318-322); Frans Voorbraak  ...  , A preferential model semantics for default logic (344-351); Emil Weydert, Elementary hyperentailment—nonmonotonic reasoning about defaults (352-359). 94f:68032 68-06 68U05 * Selected papers from the  ... 

A Tableau Method for Checking Rule Admissibility in S4

Sergey Babenyshev, Vladimir Rybakov, Renate A. Schmidt, Dmitry Tishkovsky
2010 Electronical Notes in Theoretical Computer Science  
Using a recently introduced framework for synthesising tableau decision procedures this can be turned into a sound, complete and terminating tableau calculus for the extended logic, and gives a tableau-based  ...  Our method is based on a standard semantic ground tableau approach. In particular, we reduce rule admissibility in S4 to satisfiability of a formula in a logic that extends S4.  ...  Semantic Characterisation of Admissibility We now give a semantic characterisation of admissibility in S4.  ... 
doi:10.1016/j.entcs.2010.04.003 fatcat:zsn4edxqvzaq7gyhwlzsbt4wt4

Page 802 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Summary: “The paper presents a labelled tableau system for $4.3, based on the D’Agostino, Mondadori system KE [M. D’ Agostino, in Handbook of tableau methods, 45-123, Kluwer Acad.  ...  There are two layers involved in the definition of }: at the bottom is a proposi- tional modal conditional logic which allows unlimited nesting of defaults and embeddings into any context analyzable in  ... 

Stable inference as intuitionistic validity

David Pearce
1999 The Journal of Logic Programming  
The paper characterises the nonmonotonic inference relation associated with the stable model semantics for logic programs as follows: a formula is entailed by a program in the stable model semantics if  ...  In place of intuitionistic logic, any proper intermediate logic can be used.  ...  [5] ) lntuitionistic logic can readily be presented in any of the usual 'deductive' styles, e.g. as a tableau system, a natural deduction ~ystem or as a Gentzen-style sequent calculous.  ... 
doi:10.1016/s0743-1066(98)10015-8 fatcat:yn4usv7conburpzrwgni7ta5si

Towards automated first-order abduction: the cut-based approach

M. Finger
2010 Logic Journal of the IGPL  
This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the undecidable precondition problem.  ...  We use letters p, q, r, s for atomic propositional or predicate symbols; an enumerable set of variables V ={x 1 ,x 2 ,...}; logical constants ⊥ and ; connectives ∧ (conjunction), ∨ (disjunction), ¬ (negation  ...  Poole's Default Reasoning [22] is a logical framework in which one is capable of generating explanations.  ... 
doi:10.1093/jigpal/jzq052 fatcat:4hpw27rrlvb6noqonwqcg7y4pq

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Sopo Pkhakadze, Hans Tompits
2020 Axioms  
Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which  ...  The first variant of default logic employs ukasiewicz's three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults.  ...  An Anti-Sequent Calculus for Ł 3 As for axiomatising non-theorems of Ł 3 , a systematic construction of rejection calculi for many-valued logics has been developed by Bogojeski and Tompits [27] , based  ... 
doi:10.3390/axioms9030084 fatcat:qnmunhwjcnaufiysaoa77gttci

Extended ASP Tableaux and rule redundancy in normal logic programs

2008 Theory and Practice of Logic Programming  
The proof system is based on the ASP tableaux defined in the work by Gebser and Schaub (Tableau calculi for answer set programming.  ...  proof for a family of normal logic programs {Φn} for which ASP Tableaux has exponential-length minimal proofs with respect ton.  ...  Especially, the inference techniques applied in current state-of-the-art ASP solvers have been characterised by a family of tableau-style ASP proof systems for normal logic programs only very recently  ... 
doi:10.1017/s1471068408003578 fatcat:fdqwcjviqzaiplpjpt2egippqa

Equilibrium logic

David Pearce
2006 Annals of Mathematics and Artificial Intelligence  
Equilibrium logic is a system of nonmonotonic reasoning that generalises answer set semantics for logic pro-gram~ to a syntactically broader class of theories.  ...  to the situation of a nonmonotonic underlying logic.  ...  The tableau system and abduction Having a proof system based on tableaux allows one to apply techniques for generating abductive explanations for the classical logic based on this proof system.  ... 
doi:10.1007/s10472-006-9028-z fatcat:iv4ywmgxgffjbclhugptvapad4

Automated Synthesis of Tableau Calculi

Renate Schmidt, Dmitry Tishkovsky, Martin Giese
2011 Logical Methods in Computer Science  
This paper presents a method for synthesising sound and complete tableau calculi.  ...  For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.  ...  LoTREC and the Tableau Workbench are generic systems for building tableau-based theorem provers for non-classical logics.  ... 
doi:10.2168/lmcs-7(2:6)2011 fatcat:wcvr7oon3ncjlniwxvvpd436mi

Decision procedures for some strong hybrid logics

Andrzej Indrzejczak, Michał Zawidzki
2013 Logic and Logical Philosophy  
Tableau calculus for the logic H(@, E, D, ♦ − ) Tableau calculi. Two main types of tableau calculi for hybrid logics are present in the literature, namely the prefixed and the internalised calculi.  ...  So far, several tableau calculi for hybrid logics have been presented in the literature.  ...  A part of this paper is an extended and modified version of an article by Michał Zawidzki, published in the Proceedings of the Student Session of European Summer School of Logic, Language and Information  ... 
doi:10.12775/llp.2013.022 fatcat:26kmz56lijga7asnhuqan7v5li

Page 6903 of Mathematical Reviews Vol. , Issue 2001J [page]

2001 Mathematical Reviews  
The paper is mostly concerned with comparing the efficiency of Ksat with that of other procedures, such as the tableau based Kris.  ...  A new argument, based on work of J. Stupecki and G.  ... 
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