Parallel interpolation, splitting, and relevance in belief change

Kourousias, George; Makinson, David

doi:10.2178/jsl/1191333851

Cited by 51 publications

(66 citation statements)

References 6 publications

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Order By: Relevance

“…UCR3 is its counterpart of CR1-CR2 in our framework, and it can be seen as a counterpart of the relevance criterion [19]. It says that in case two elements are incomparable in the input, then the ordering between these two elements should be the same in both initial state and revised state.…”

Section: Additional Postulatesmentioning

confidence: 99%

Revision over Partial Pre-orders: A Postulational Study

Benferhat

Liu

2012

Lecture Notes in Computer Science

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Abstract. Belief revision is the process that incorporates, in a consistent way, a new piece of information, called input, into a belief base. When both belief bases and inputs are propositional formulas, a set of natural and rational properties, known as AGM postulates, have been proposed to define genuine revision operations. This paper addresses the following important issue : How to revise a partially pre-ordered information (representing initial beliefs) with a new partially pre-ordered information (representing inputs) while preserving AGM postulates? We first provide a particular representation of partial pre-orders (called units) using the concept of closed sets of units. Then we restate AGM postulates in this framework by defining counterparts of the notions of logical entailment and logical consistency. In the second part of the paper, we provide some examples of revision operations that respect our set of postulates. We also prove that our revision methods extend well-known lexicographic revision and natural revision for both cases where the input is either a single propositional formula or a total pre-order.

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Section: Additional Postulatesmentioning

confidence: 99%

Revision over Partial Pre-orders: A Postulational Study

Benferhat

Liu

2012

Lecture Notes in Computer Science

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“…Our original result in Parikh (1999) considered only the case where L is finite. Kourousias and Makinson (2007) extended this result to the case where L is infinite.…”

Section: Belief Revisionmentioning

confidence: 89%

“…Also, T is confined to the language {P, Q, R} and knows nothing about S. Note that Q and R are entangled and cannot be separated. Lemma 2.1(Kourousias and Makinson 2007;Parikh 1999): Given a theory T in the language L, there is a unique finest T -splitting of L, i.e. one which refines every other T -splitting.…”

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confidence: 99%

Beth definability, interpolation and language splitting

Parikh

2010

Synthese

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Both the Beth definability theorem and Craig's lemma (interpolation theorem from now on) deal with the issue of the entanglement of one language L 1 with another language L 2 , that is to say, information transfer-or the lack of such transfer-between the two languages. The notion of splitting we study below looks into this issue. We briefly relate our own results in this area as well as the results of other researchers like Kourousias and Makinson, and Peppas, Chopra and Foo. Section 3 does contain one apparently new theorem.

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“…(3) Note that when the finest splitting E = {E i } i∈I of K has at least two cells, then K # cannot be closed under classical consequence -the conjunction of any two formulae from different cells will be in Cn(K # ) but cannot be in K # . Even when there is only one cell, K # need not be closed under consequence.…”

Section: Background On Partitionsmentioning

confidence: 99%

“…We begin by reviewing the state of play, focussing on the operation of contraction (thus leaving aside revision) and omitting all proofs (which can be found in Kourousias and Makinson [3]). Definition 6.1.…”

Section: Respecting Relevance In Belief Changementioning

confidence: 99%

Propositional relevance through letter-sharing

Makinson

2009

Journal of Applied Logic

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The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones.From syntactic to canonical cell/path relevance Logical relevance as a two-place relation between formulaeAttempts to give formal expression to the notion of relevance between propositional formulae go back at least to Belnap [2], who suggested that a necessary, but not sufficient, condition for one formula to be relevant to another is that they share some elementary letter. We call this syntactical relevance. Definition 1.1. Let a, b be formulae of a given propositional logic. They are syntactically relevant to each other iff they share some elementary letter.In the same paper, Belnap went on to propose that relevance of antecedent to consequent should serve as an adequacy condition for any acceptable entailment relation in propositional logic. While classical logic fails syntactic relevance, his subclassical logic E (for 'entailment') satisfies that formal condition, as do a number of other subsystems of classical logic that came to be known as 'relevance logics'.The present paper is not at all concerned with such relevance logics, and we have no desire to weaken the classical one. We are interested in the concept of relevance itself. Our purpose is to see how far the simple idea of letter-sharing may be developed into a well-behaved formal account of relevance in classical propositional contexts, and examine its application to the theory of belief change.Poor behaviour of syntactic relevance. (1) The relation is syntax-dependent. In other words, formulae a, b may be classically equivalent to a , b respectively, and a relevant to b but a not relevant to b . Moreover (2), for any a, b there are a , b to which they are respectively classically equivalent, with a syntactically relevant to b . Example 1.1. For (1), the formula ¬p ∧ (¬p ∨ q) is syntactically relevant to q, but the former is classically equivalent to ¬p which is not relevant to ...

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Parallel interpolation, splitting, and relevance in belief change

Cited by 51 publications

References 6 publications

Revision over Partial Pre-orders: A Postulational Study

Revision over Partial Pre-orders: A Postulational Study

Beth definability, interpolation and language splitting

Propositional relevance through letter-sharing

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