Beliefs have been formally modelled in the last decades using doxastic logics. The possible worlds model and its associated Kripke semantics provide an intuitive semantics for these logics, but they seem to commit us to model agents that are logically omniscient (they believe every classical tautology) and perfect reasoners (their beliefs are closed under classical deductive closure). Thus, thi...

Lewis (1981) showed the equivalence between two dominant semantic frameworks for counterfactuals: ordering semantics, which relies on orders between possible worlds, and premise semantics, which relies on sets of propositions (so-called ordering sources). I define a natural, restricted version of premise semantics, expressible premise semantics, which is based on ordering sources containing onl...

The semantics for counterfactuals due to David Lewis has been challenged on the basis of unlikely, or impossible, events. Such events may skew a given similarity order in favour of those possible worlds which exhibit them. By updating the relational structure of a model according to a ceteris paribus clause one forces out, in a natural manner, those possible worlds which do not satisfy the requ...

We investigate probability logic with the conditional probability operators. This logic, denoted LCP , allows making statements such as: P sα, CP s(α | β), CP 0(α | β) with the intended meaning “the probability of α is at least s”, “the conditional probability of α given β is at least s”, “the conditional probability of α given β at most 0”. A possible-world approach is proposed to give semanti...

We extend the theory about terminological default reasoning by using a logical base language that can represent spatioterminological phenomena. Based on this description logic language called ALCRP(S2), which is briefly introduced, we discuss algorithms for computing so-called extensions (“possible worlds”) of a world description and a set of defaults. We conclude with an application of the the...

In this paper we investigate a probability logic with conditional probability operators. The logic (denoted LPP ) allows making statements such as CP≥s(α | β), with the intended meaning ”the conditional probability of α given β is at least s”. Conditional probabilities are defined in the usual Kolmogorv style: P (α | β) = P (α∧β) P (β) , P (β) > 0. A possible-world approach is used to give sema...

We introduce a new approach to representing and manipulating various types of non-singular concepts in natural language discourse. The representation we describe is based on a partially ordered structure of levels in which the objects of the same relative singularity are assigned to the same level. Our choice of the representation has been motivated by the following main concerns: I. The repres...

The label semantics linguistic representation framework is introduced as an alternative approach to computing and modelling with words, based on the concept of appropriateness rather than graded truth. A possible worlds interpretation of label semantics is then proposed. In this model it is shown that certain assumptions about the underlying possible worlds can result in appropriateness measure...

This paper describes a formal framework for uncertain reasoning in the possible worlds semantic theory. It shows that the model theory of belief functions is simpler than the model theory of lower order monotonic capacities. We concentrate on finding a generalization of belief functions with the same simple model theory, which also admits a conjunction operator. We identify collections of belie...

The semantics of evidentials is often analyzed as a subcase or a special case of modality in the recent formal literature (Izvorski, 1997; Faller, 2002; Speas, to appear; McCready and Ogata, 2005, among others). Moreover, some modern linguists consider the analysis of modality as a subcase of evidential or a speech act modifier (Papafragou 2000; Huddleston and Pullum 2002; Drubig 2001, among ot...