Analytic Tableaux Calculi for KLM Logics of Nonmonotonic Reasoning

Journal of Logic and Computation, 2002

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE + -a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof-that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.

The tableau-like proof system KEM has been proven to be able to cope with a wide variety of (normal) modal logics. KEM is based on D'Agostino and Mondadori's (1994) classical proof system KE, a combination of tableau and natural deduction inference rules which allows for a ...

Logics in Artificial Intelligence, 1996

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 and Doyle's logics and ground logics. It also achieves the computational complexity lower bounds.

Lecture Notes in Computer Science, 2006

In this paper we present a tableau calculus for the rational logic R of default reasoning, introduced by Kraus, Lehmann and Magidor. Our calculus is obtained by introducing suitable modalities to interpret conditional assertions, and makes use of labels to represent possible worlds. We also provide a decision procedure for R, and study its complexity.

In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The label formalism introduced in [AG94,ABGR96] to account for the semantics of normal modal logics is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the propositional system KE +-a tableau-like analytic proof system devised to be used both as a refutation and a direct method of proof-enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.

2003

In this paper we develop labelled and uniform tableau methods for some fundamental system of propositional conditional logics. We consider the well-known system CE (that can be seen as a generalization of preferential nonmonotonic logic), and some related systems. Our tableau proof procedures are based on a possible-worlds structures endowed with a family of preference relations. The tableau procedure gives the first practical decision procedure for CE.

arXiv: Logic, 2016

In this paper we present analytic tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a syntactic proof of cut elimination. We also show the subformula property for our tableaux, and prove the decidability of justification logics for finite constant specifications.

2010

In this paper, we propose the logic Pmin , which is a nonmonotonic extension of Preferential logic P defined by Kraus, Lehmann and Magidor (KLM). In order to perform nonmonotonic inferences, we define a “minimal model” semantics. Given a modal interpretation of a minimal A-world as A ∧ □¬A, the intuition is that preferred, or minimal models are those that minimize the number of worlds where ¬□¬A holds, that is of A-worlds which are not minimal. We also present a tableau calculus for deciding entailment in Pmin .

2010

Abstract. In this paper, we propose the logic Pmin, which is a non-monotonic extension of Preferential logic P defined by Kraus, Lehmann and Magidor (KLM). In order to perform nonmonotonic inferences, we define a “minimal model ” semantics. Given a modal interpretation of a minimal A-world as A ∧ ¬A, the intuition is that preferred, or mini-mal models are those that minimize the number of worlds where ¬¬A holds, that is of A-worlds which are not minimal. We also present a tableau calculus for deciding entailment in Pmin. 1

Lecture Notes in Computer Science, 2000

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM , introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the propositional system KE + -a tableau-like analytic proof system devised to be used both as a refutation and a direct method of proof-enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications. R. Dyckhoff (eds)