We give a general framework for developing the least model semantics, xpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. 8x 9y R i (x; y)) and some classical rst-order Horn formulas. Our approach is direct and no restriction on occurrences of 2 i and 3 i is required. We apply the framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T , B, 4, 5 (in the form, e.g., 4 : 2 i ! 2 j 2k) and I : 2 i ! 2 j . Another part of the work is devoted to programming in multimodal logics intended for reasoning about multi-degree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multi-agent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more eective.

We give formulations for modal deductive databases and present a modal query language called MDatalog. We define modal relational algebras and give the seminaive evaluation algorithm, the top-down evaluation algorithm, and the magic-set transformation for MDatalog queries. The results of this paper like soundness and completeness of the top-down evaluation algorithm or correctness of the magic-set transformation are proved for the multimodal logics of belief KDI4s5, KDI45, KD4s5s, KD45(m), KD4Ig5a, and the class of serial contextfree grammar logics. We also show that MDatalog has PTIME data complexity in the logics KDI4s5, KDI45, KD4s5s, and KD45(m). 1

The study of embodied communication requires access to multiple data sources such as multistream video and audio, various derived and meta-data such as gesture, head, posture, facial expression and gaze information. This thesis presents the data collection, annotation, and analysis for multiple participants engaged in planning meetings. In support of the analysis tasks, this thesis presents the multimedia Visualization for Situated Temporal Analysis for Macintosh (MacVisSTA) system. It supports the analysis of multimodal human communication through the use of video, audio, speech transcriptions, and gesture and head orientation data. The system uses a multiple linked representation strategy in which different representations are linked by the current time focus. MacVisSTA supports analysis of the synchronized data at varying timescales for coarse-to-fine observational studies. The hybrid architecture may be extended through plugins. Finally, this effort has resulted in encoding of behavioral and language data, enabling collaborative research and embodying it with the aid of, and interface to, a database management system. ii

Abstract. Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLD-resolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended for reasoning about belief and common belief of agents. We prove that the presented SLD-resolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4Ig5a. This shows that it is worth to study modal logic programming for multi-agent systems. 1

Abstract. We develop semantics for modal logic programs in basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4,5(intheform,e.g., 4:✷iϕ → ✷j✷kϕ) andI: ✷iϕ → ✷jϕ. We do not assume any special restriction for the form of programs and goals. Our fixpoint semantics and SLD-resolution calculus are defined using the direct approach and closely reflect the axioms of the used modal logic. We prove that our SLD-resolution calculus is sound and complete. 1

ABSTRACT. We present optimizations for the modal logic programming system MProlog, including the standard form for resolution cycles, optimized sets of rules used as meta-clauses, optimizations for the version of MProlog without existential modal operators, as well as iterative deepening search and tabulation. Our SLD-resolution calculi for MProlog in a number of modal logics are still strongly complete when resolution cycles are in the standard form and optimized sets of rules are used. We also show that the labelling technique used in our direct approach is relatively better than the Skolemization technique used in the translation approaches for modal logic programming. KEYWORDS: modal logic, logic programming, MProlog. DOI:10.3166/JANCL.19.167–181 c ○ 2009 Lavoisier, Paris