This article discusses pragmatic aspects of our interpretation of intensional constructions like questions and propositional attitude reports. In the first part, it argues that our evaluation of these constructions may vary relative to the identification methods operative in the context of use. This insight is then given a precise formalization in a possible world semantics. In the second part,...

This paper begins with the assumption that possible worlds and times are represented as situation pronouns in natural language (see Cresswell, 1990; Percus, 2000; Kusumoto, 2005; Keshet, 2008). For simplicity, situations are construed to be world-time pairs, and a predicate taking such a pair as an argument is evaluated in the world and the time specified. Researchers such as Percus (2000) have...

In this paper, we extend Nilsson’s probabilistic logic [1] to allow that each sentence S has three sets of possible worlds. We adopt the ideas of consistency and possible worlds introduced by Nilsson in [1], but propose a new method called linear equation method to deal with the problems of probabilistic inference, the results of our method is consistent with those of Yao’s interval-set model m...

Players’ beliefs may be incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require players’ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. We show that common c...

Fine and Kripke extended S5, S4, S4.2 and such to produce propositionally quantified systems S5π+, S4π+, S4.2π+: given a Kripke frame, the quantifiers range over all the sets of possible worlds. S5π+ is decidable and, as Fine and Kripke showed, many of the other systems are recursively isomorphic to second-order logic. In the present paper I consider the propositionally quantified system that a...

The question now arises how the two kinds of alethic modalities relate to each other. The answer, of course, depends on how precisely we characterize the two notions. Suppose that we have a class K consisting of all Kripke models for a language of modal propositional or predicate logic with operators: Ø for metaphysical necessity, L for logical necessity, and A for actuality. Each model is asso...

Incidence calculus is a mechanism for probabilistic reasoning in which sets of possible worlds called incidences are associated with axioms and probabilities are then associated with these sets Inference rules are used to deduce bounds on the incidences of formulae which are not axioms and bounds for the probability of such a formula can then be obtained In practice an assignment of probabiliti...

The evaluation of an implication by Imaging is a logical technique developed in the framework of modal logic. Its interpretation in the context of a \possible worlds" semantics is very appealing for IR. In 1989, Van Rijsbergen suggested its use for solving one of the fundamental problems of logical models in IR: the evaluation of the implication d! q (where d and q are respectively a document a...

In no possible world does a time traveler succeed in killing her earlier self before she ever enters a time machine. So if many, many time travelers went back in time trying to kill their unprotected former selves, the time travelers would fail in many strange, “coincidental” ways, slipping on banana peels, killing the wrong victim, and so on. Such cases produce doubts about time travel. How co...

We consider the problem of incorporating end-user advice into reinforcement learning (RL). In our setting, the learner alternates between practicing, where learning is based on actual world experience, and end-user critique sessions where advice is gathered. During each critique session the end-user is allowed to analyze a trajectory of the current policy and then label an arbitrary subset of t...