Received 12 December 2013 1991 Mathematics Subject Classification: 03G25; 06D05

Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truthfunctional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congru...

Forthcoming in the Journal of Aritificial Intelligence We introduce mathematical programming and atomic decomposition as the basic modal (T-Box) inference techniques for a large class of modal and description logics. The class of description logics suitable for the proposed methods is strong on the arithmetical side. In particular there may be complex arithmetical conditions on sets of accessib...

This paper extends a programming language for implementing cognitive agents with the capability to explicitly represent beliefs and reason about them. In this programming language, the beliefs of agents are implemented by modal logic programs, where beliefs are represented by explicit modal operators. A distinction is made between a belief base language that can be used to represent an agent’s ...

Let L be a language containing the modal operator B – for full belief. An information model is a set E of stable L-theories ([19], [21], [30], [27]). A sentence is valid if it is accepted in all theories of every model. We show that a formula A is valid if and only if it is a theorem of the modal system S5. The second part of the paper considers the possibility of providing probabilistic founda...

The epistemic modals possible, probable, likely, and certain require a semantics which treats them both as modal operators and as gradable adjectives. An analysis of these items in terms of Kennedy & McNally (2005)’s theory gradability suggests that they are associated with a single, fully closed scale of possibility. An implementation using the standard (Kratzerian) theory of modality is shown...

In this paper we present a general methodology to extend Defeasible Logic with modal operators. We motivate the reasons for this type of extension and we argue that the extension will allow for a robust knowledge framework in different application areas. The paper presents an extension of RuleML to capture Modal Defeasible Logic.

We define two modal logics that allow to reason about modifications of graphs. Both have a universal modal operator. The first one only involves global modifications (of some state label, or of some edge label) everywhere in the graph. The second one also allows for modifications that are local to states. The global version generalizes logics of public announcements and public assignments, as w...

In this paper, we consider the influence of trust on the assimilation of acquired information into an agent’s belief. By use of modal logic tools, we characterize the relationship among belief, information acquisition and trust both semantically and axiomatically. The belief and information acquisition are respectively represented by KD45 and KD normal modal operators, whereas trust is expresse...