this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ffl-semantics, possibilistic structures, and -rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:

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.

Belief change is a fundamental problem in AI: Agents constantly have to update their beliefs to accommodate new observations. In recent years, there has been much work on axiomatic characterizations of belief change. We claim that a better understanding of belief change can be gained from examining appropriate semantic models. In this paper we propose a general framework in which to model belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes OE if he knows that OE is more plausible than :OE. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagi...

tions beliefs. We say that an agent believes ' if she acts as though ' is true. As time passes and new evidence is observed, changes in an agent's defeasible assumptions lead to changes in her beliefs. Thus, the question of belief change---that is, how beliefs change over time---is a central one for understanding systems that can make and modify defeasible assumptions. In this dissertation, we propose a new approach to the question of belief change. This approach is based on developing a semantics for beliefs. This semantics is embedded in a framework that models agents' knowledge (or information) as well as their beliefs, and how these change in time. We argue, and demonstrate by examples, that this framework can naturally model any dynamic system (e.g., agents and their environment). Moreover, the framework allows us to consider what the properties of well-behaved belief change should be. As we show, such a framework can g

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In this paper we analyse some logical notions relevant for representing the dynamics of institutionalised organisations. In particular, some well-known action concepts introduced in the Kanger-Lindahl-Pörn logical theory of agency are discussed and integrated. Secondly, moving from the work of Jones and Sergot, a logical characterisation is provided of the ideas of institutional links, “counts-as” connections, and institutional facts. This approach is then enriched by a new modal operator proc, intended to account for the autonomous and decentralised creation of new institutional facts and normative positions within institutions.

We offer a system to capture the relationship between knowledge and belief, which also sheds new light on each of them in isolation. In the case of knowledge, we strongly reject the property of negative introspection. In the case of belief, we propose a distinction between belief (whose defeasibility is recognized by the agent) and certainty (whose defeasibility is not). The relationship between the three notions -- knowledge, certainty, and belief -- goes far beyond mere hierarchy. In particular, knowledge has the flavor of belief that is stable under incorporation of correct facts. We explore these first through a model theory, which is based on the notions of the agent's subconscious biases and its conscious preferences (or plausibility measure). We then provide a sound and complete axiomatic system, and point to some of its illuminating properties. We compare our construction to previous ones in AI and philosophy, and in particular point to connections with recent work in AI based ...

In this paper, we survey some quantitative and qualitative approaches to uncertainty management based on possibility theory and present a logical framework to integrate them. The semantics of the logic is based on the Dempster's rule of conditioning for possibility theory. It is then shown that classical modal logic, conditional logic, possibilistic logic, quantitative modal logic and qualitative possibilistic logic are all sublogics of the present logical framework. In this way, we can formalize and generalize some well-known results about possibilistic reasoning in a uniform semantics. Moreover, our uniform framework is applicable to nonmonotonic reasoning, approximate consequence relation formulation, and partial consistency handling. Key words: Non-classical logics, possibility theory, conditional possibility, modal logic, conditional logic. 1 Introduction There are essentially two kinds of logical formalisms for reasoning about possibility and necessity. On the one hand, the qua...

Abstract We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourrón, Gärdenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove’s construction based on total pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gärdenfors’s triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott’s E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and we study their complexity. 1