Category: modal logic

Modal logic: developments & applications in IT research areas

This post contains preliminary and very general research into recent developments in nonclassical (i.e. modal) logics and information technology and other relevant areas of study (namely, knowledge representation, computer programming, decision theory, artificial intelligence, verificationism)

A modal logic framework for multi-agent belief fusion

Liau, C. 2005. A modal logic framework for multi-agent belief fusion. ACM Trans. Comput. Logic 6, 1 (Jan. 2005), 124-174. DOI=

Epistemic logic, belief fusion, belief revision, database merging, multi-agent systems, multi-sources reasoning


This article provides a modal logic framework for reasoning about multi-agent belief and its fusion. We propose logics for reasoning about cautiously merged agent beliefs that have different degrees of reliability. These logics are obtained by combining the multi-agent epistemic logic and multi-source reasoning systems. The fusion is cautious in the sense that if an agent’s belief is in conflict with those of higher priorities, then his belief is completely discarded from the merged result. We consider two strategies for the cautious merging of beliefs. In the first, called level cutting fusion, if inconsistency occurs at some level, then all beliefs at the lower levels are discarded simultaneously. In the second, called level skipping fusion, only the level at which the inconsistency occurs is skipped. We present the formal semantics and axiomatic systems for these two strategies and discuss some applications of the proposed logical systems. We also develop a tableau proof system for the logics and prove the complexity result for the satisfiability and validity problems of these logics.


An internal semantics for modal logic

Fagin, R. and Vardi, M. Y. 1985. An internal semantics for modal logic. In Proceedings of the Seventeenth Annual ACM Symposium on theory of Computing (Providence, Rhode Island, United States, May 06 – 08, 1985). STOC ’85. ACM, New York, NY, 305-315. DOI=


In Kripke semantics for modal logic, “possible worlds” and the possibility relation are both primitive notions. This has both technical and conceptual shortcomings. From a technical point of view, the mathematics associated with Kripke semantics is often quite complicated. From a conceptual point of view, it is not clear how to use Kripke structures to model knowledge and belief, where one wants a clearer understanding of the notions that are primitive in Kripke semantics. We introduce modal structures as models for modal logic. We use the idea of possible worlds, but by directly describing the “internal semantics” of each possible world. It is much easier to study the standard logical questions, such as completeness, decidability, and compactness, using modal structures. Furthermore, modal structures offer a much more intuitive approach to modelling knowledge and belief.

First-order classical modal logic: applications in logics of knowledge and probability

Arló-Costa, H. and Pacuit, E. 2005. First-order classical modal logic: applications in logics of knowledge and probability. In Proceedings of the 10th Conference on theoretical Aspects of Rationality and Knowledge (Singapore, June 10 – 12, 2005). R. van der Meyden, Ed. Theoretical Aspects Of Rationality And Knowledge. National University of Singapore, Singapore, 262-278.

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. We conclude by offering a general completeness result for the entire family of first order classical modal logics (encompassing both normal and non-normal systems).