2,768 research outputs found
AGM-Like Paraconsistent Belief Change
Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations
Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics
Belief revision of knowledge bases represented by a set of sentences in a
given logic has been extensively studied but for specific logics, mainly
propositional, and also recently Horn and description logics. Here, we propose
to generalize this operation from a model-theoretic point of view, by defining
revision in an abstract model theory known under the name of satisfaction
systems. In this framework, we generalize to any satisfaction systems the
characterization of the well known AGM postulates given by Katsuno and
Mendelzon for propositional logic in terms of minimal change among
interpretations. Moreover, we study how to define revision, satisfying the AGM
postulates, from relaxation notions that have been first introduced in
description logics to define dissimilarity measures between concepts, and the
consequence of which is to relax the set of models of the old belief until it
becomes consistent with the new pieces of knowledge. We show how the proposed
general framework can be instantiated in different logics such as
propositional, first-order, description and Horn logics. In particular for
description logics, we introduce several concrete relaxation operators tailored
for the description logic \ALC{} and its fragments \EL{} and \ELext{},
discuss their properties and provide some illustrative examples
Belief merging within fragments of propositional logic
Recently, belief change within the framework of fragments of propositional
logic has gained increasing attention. Previous works focused on belief
contraction and belief revision on the Horn fragment. However, the problem of
belief merging within fragments of propositional logic has been neglected so
far. This paper presents a general approach to define new merging operators
derived from existing ones such that the result of merging remains in the
fragment under consideration. Our approach is not limited to the case of Horn
fragment but applicable to any fragment of propositional logic characterized by
a closure property on the sets of models of its formulae. We study the logical
properties of the proposed operators in terms of satisfaction of merging
postulates, considering in particular distance-based merging operators for Horn
and Krom fragments.Comment: To appear in the Proceedings of the 15th International Workshop on
Non-Monotonic Reasoning (NMR 2014
PSPACE Bounds for Rank-1 Modal Logics
For lack of general algorithmic methods that apply to wide classes of logics,
establishing a complexity bound for a given modal logic is often a laborious
task. The present work is a step towards a general theory of the complexity of
modal logics. Our main result is that all rank-1 logics enjoy a shallow model
property and thus are, under mild assumptions on the format of their
axiomatisation, in PSPACE. This leads to a unified derivation of tight
PSPACE-bounds for a number of logics including K, KD, coalition logic, graded
modal logic, majority logic, and probabilistic modal logic. Our generic
algorithm moreover finds tableau proofs that witness pleasant proof-theoretic
properties including a weak subformula property. This generality is made
possible by a coalgebraic semantics, which conveniently abstracts from the
details of a given model class and thus allows covering a broad range of logics
in a uniform way
A recovery operator for nontransitive approaches
In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities
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