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1

Rough Dialogue and Implication Lattices

Chakraborty M.K., Banerjee M.

Fundamenta Informaticae

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2007

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Vol. 75, nr 1-4

123-139

EN

A dialogue is an `activity' by a pair of agents to arrive at some kind of understanding over a concept/belief/piece of information etc. represented by a subset (the extension) in some universe of discourse. The universe is partitioned into two different sets of granules (equivalence classes) representing the perceptions of the agents. So, there are two approximation spaces at the beginning. A third approximation space arises out of superimposition of the two partitions. A dialogue is a finite process of gradual enhancement of the two base subsets of the agents, in their `common' approximation space. Through this process, various kinds of overlap may emerge between the two final subsets. A first introduction of the idea of a dialogue in rough context was made in [6]. This paper further develops the notion and focusses upon the study of the above-mentioned overlaps in a systematic manner. Given two sets A and B in an approximation space, there are nine possible inclusion relations among the sets lo(A), A, up(A), lo(B), B and up(B) where lo and up denote the lower and upper approximation operators respectively. There are five resulting equivalence classes and the quotient set forms a lattice by implication ordering. That is, of the nine relations, only five are independent and they form an implication or entailment lattice. Starting with this basic lattice other implication lattices are formed. Relationship of these lattices with the various overlap conditions between the final pair of sets arrived at after a dialogue is studied. Finally, examples are given, one of which relates dialogues in rough context with rough belief revision [3] - in a line similar to the approach of [5].

2

The Compactness of Belief Revision and Update Operators

Liberatore P., Schaerf M.

Fundamenta Informaticae

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2004

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Vol. 62, nr 3,4

377--393

EN

A propositional knowledge base can be seen as a compact representation of a set of models. When a knowledge base T is updated with a formula P, the resulting set of models can be represented in two ways: either by a theory T' that is equivalent to T*P or by the pair ‹T,P›. The second representation can be super-polinomially more compact than the first. In this paper, we prove that the compactness of this representation depends on the specific semantics of *, , Winslett's semantics is more compact than Ginsberg's.

3

Modal Probability, Belief, and Actions

Herzig A.

Fundamenta Informaticae

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2003

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Vol. 57, nr 2-4

323--344

EN

We investigate a modal logic of probability with a unary modal operator expressing that a proposition is more probable than its negation. Such an operator is not closed under conjunction, and its modal logic is therefore non-normal. Within this framework we study the relation of probability with other modal concepts: belief and action. We focus on the evolution of belief, and propose an integration of revision. For that framework we give a regression algorithm.

4

Changing and using beliefs under incomplete information

Jamroga W.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2001

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Nr 928

31-36

EN

The concept being proposed here is to use prototype semantics to represent an agent's belief state. Prototype semantics is a linguistic theory that emerged in the 1980s - the key idea is to describe the meaning of an utterance, or a notion, by defining the prototype (the most typical example to which the notion refers) and the extension rules describing 'family resemblances' between various entities and, in consequence, allowing to derive less typical instances from more typical ones. The intuition behind this paper is that in situations of incomplete information such a representation of the agent's knowledge may be easier to deal with than a straightforward probabilistic representation - especially when belief changes are not necessarily monotonic, and informations being acquired by the agent may be vague themselves. Moreover, when an exhaustive search through all the possibilities is impossible the agent may benefit from analyzing the typical situations instead of random ones. This property was tested for a family of games with incomplete information on binary trees.

5

Credibility of information for modelling belief state and its change

Gomolińska A.

Fundamenta Informaticae

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1998

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Vol. 34, nr 1,2

33-51

EN

Credibility of information is investigated for the purpose of modelling belief state and its change.