In (Petrick and Bacchus 2002), a “knowledge-level” approach to planning under incomplete knowledge and sensing was presented. In comparison with alternate approaches based on representing sets of possible worlds, this higher-level representation is richer, but the inferences it supports are weaker. Nevertheless, because of its richer representation, it is able to solve problems that cannot be s...

The possible worlds model and its associated Kripkean semantics provide an intuitive semantics to epistemic logics, but they seem to commit us to model agents which are logically omniscient and perfect reasoners. In this article we show that this is not necessarily the case, if possible worlds are not considered as consistent descriptions of the real world. We propose to model the beliefs of an...

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such...

Observing the actions of other people allows us to learn not only about their mental states, but also about hidden aspects of a shared environmental situation – things we cannot see, but they can, and that influence their behavior in predictable ways. This paper presents a computational model of how people can learn about the world through these social inferences, supported by the same Theory o...

Invariance is one of the most important notions in applications of mathematics. It is one of the key concepts in modern physics, is a computational tool that helps in solving complex equations, etc. In view of its importance, it is desirable to come up with a definition of invariance which is as general as possible. In this paper, we describe how to formulate a general notion of invariance in c...

In this paper we consider a logic programming framework for reasoning about imprecise probabilities. In particular, we propose a new semantics, for the Probabilistic Logic Programs (p-programs) of Ng and Subrahmanian. Pprograms represent imprecision using probability intervals. Our semantics, based on the possible worlds semantics, considers all point probability distributions that satisfy a gi...

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...