This paper combines various structures representing degrees of belief, degrees of disbelief, and degrees of non-belief (degrees of expectations) into a unified whole. The representation uses relations of comparative necessity and possibility, as well as non-probabilistic functions assigning numerical values of necessity and possibility. We define all-encompassing necessity structures which have weak expectations (mere hypotheses, guesses, conjectures, etc.) occupying the lowest ranks and very strong, ineradicable ('a priori') beliefs occupying the highest ranks. Structurally, there are no differences from the top (...) to the bottom. I argue that belief is a vague notion, and that thresholds for belief, if there are any, are context-dependent. (shrink)

The aim of this paper is to propose a formal approach to reasoning about desires, understood as logical propositions which we would be pleased to make true, also acknowledging the fact that desire is a matter of degree. It is first shown that, at the static level, desires should satisfy certain principles that differ from those to which beliefs obey. In this sense, from a static perspective, the logic of desires is different from the logic of beliefs. While the accumulation (...) of beliefs tend to reduce the remaining possible worlds they point at, the accumulation of desires tends to increase the set of states of affairs tentatively considered as satisfactory. Indeed beliefs are expected to be closed under conjunctions, while, in the positive view of desires developed here, one can argue that endorsing \ as a desire means to desire \ and to desire \. However, desiring \ and \ at the same time is not usually regarded as rational, since it does not make much sense to desire one thing and its contrary at the same time. Thus when a new desire is added to the set of desires of an agent, a revision process may be necessary. Just as belief revision relies on an epistemic entrenchment relation, desire revision is based on a hedonic entrenchment relation satisfying other properties, due to the different natures of belief and desire. While epistemic entrenchment relations are known to be qualitative necessity relations, hedonic relations obeying a set of reasonable postulates correspond to another set-function in possibility theory, called guaranteed possibility, that drive well-behaved desire revision operations. Then the general framework of possibilistic logic provides a syntactic setting for encoding desire change. The paper also insists that desires should be carefully distinguished from goals. (shrink)

Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, we (...) compare the relational semantics of epistemic logics with simpler possibilistic semantics of a fragment of such logics that only uses modal formulas of depth 1. This minimal epistemic logic handles both all-or-nothing beliefs and explicitly ignored facts. We also contrast epistemic logic with the S5-based rough set logic. Finally, this paper presents extensions of generalized possibilistic logic with objective and non-nested multimodal formulas, in the style of modal logics KD45 and S5. (shrink)

Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original representation by preferential models. In this paper, we shall characterize them with a class of total preorders of formulas by improving and extending G ̈ardenfors and Makinson’s results f or expectation inference relations. A second representation is application-oriented and is obtained by considering a class of consequence (...) operators that grade sets of defaults according to our reliance on them. The finitary fragment of this class of consequence operators has been employed by recent default logic formalisms based on maxiconsistency. (shrink)