Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13]. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in [10], while the latter has been advocated by Y. Shoham in [38]. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in [2]. The pr...

Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for formulas with arbitrary nesting. 1 INTRODUCTION The study of conditional statements of the form "If : : : then : : :" has a long history in philosophy [Sta68, Lew73, Che80, Vel8...

We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new finestructure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering of interesting new questions.

ABSTRACT. We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.

A stratified view of causal reasoning is set forth; one in which the identification of counterfactual dependencies plays an important role in determining what sort of causal connection, if any, exists between two events named by a given pair of partial descriptions. A semantics for temporal counterfactuals in which events are represented at the object level is then formalized based on a syntactic form of belief updating. Counterfactuals are evaluated relative to an agent's information state, taken to include a set of initial beliefs together with additional assumptions to handle the frame problem. Inertial inferences emerge as a side-effect of requiring minimal information change between states of the world in some chronicle. A chronicle is, in addition, assumed minimal with respect to an explanatory preference that minimizes the set of beliefs that are not part of an agent's initial set of beliefs or are not supported by some body of law-like knowledge. A number of epistemic preferenc...

This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.

Preference is a basic notion in human behaviour, underlying such varied phenomena as individual rationality in the philosophy of action and game theory, obligations in deontic logic (we should aim for the best of all possible worlds), or collective decisions in social choice theory. Also, in a more

This paper is a presentation of a status quaestionis, to wit of the problem of the interpretability logic of all reasonable arithmetical theories. We present both the arithmetical side and the modal side of the question.

We present a generalization of Segerberg’s onion semantics for belief revision, in which the linearity of the spheres need not occur. The resulting logic is called broccoli logic. We provide a minimal relational logic, introducing a new neighborhood semantics operator. We then show that broccoli logic is a well-known conditional logic, the Burgess-Veltman minimal conditional logic. Belief revision is the study of theory change in which a set of formulas is ascribed to an agent as a belief set revisable in the face of new information. A dominant paradigm in belief revision is the so-called AGM paradigm, which describes a functional notion of revision (cf. [1]). A natural semantics in terms of sphere systems (cf. [6]) was given by Grove in [5] and a logical axiomatization was extensively studied by Segerberg (cf. [9, 10, 11, 12] and the forthcoming [13]). The resulting logic is called “dynamic doxastic logic ” (DDL). A generalization of the AGM approach in which revision is taken to be relational rather

This thesis develops a cognitive linguistic approach to language comprehension. The cognitive approach differs from traditional linguistic approaches in that linguistic description is seen as an integral part of the description of cognition, and that the object of description is the nature of conceptual structures, the processes which relate these conceptual structures, and the effect of context upon these processes. As a cognitive description within cognitive science, a computational approach is adopted: language comprehension is described in terms of two modules, a linguistic processing module and a discourse processing module. Within these modules, conceptual structures and processes are given a uniform characterization: structures are characterized as partial objects which are extended by processes into (potentially) less partial objects. In the linguistic processing module, linguistic expressions are characterized as signs which combine as head and modifier. The conceptual structu...