. This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion. Categories: Temporal and Modal Logic Programming. 1 Introduction In logic programming, a program is a set of Horn clauses representing our knowledge and assumptions about some problem. The semantics of logic programs as developed by van Emden and Kowalski [96] is based on the notion of the least (minimum) Herbrand model and its fixed-point characterization. As logic programming has been applied to a growing number of problem domai...

TRELLIS provides an interactive environment that allows users to add their observations, opinions, and conclusions as they analyze information by making semantic annotations about on-line documents. TRELLIS includes a vocabulary and markup language for semantic annotations of decisions and tradeoffs, and allows users to extend this vocabulary with domain specific terms or constructs that are useful to their particular task. To date, we have used TRELLIS with a variety of scenarios to annotate tradeoffs and decisions (e.g., military planning), organize materials (e.g., search results), analyze disagreements and controversies on a topic (e.g., intelligence analysis), and handle incomplete and conflicting information (e.g., genealogy research).

We present sound, (weakly) complete and cut-free tableau systems for the propositional normal modal logics S4:3, S4:3:1 and S4:14. When the modality 2 is given a temporal interpretation, these logics respectively model time as a linear dense sequence of points; as a linear discrete sequence of points; and as a branching tree where each branch is a linear discrete sequence of points. Although cut-free, the last two systems do not possess the subformula property. But for any given finite set of formulae X the "superformulae" involved are always bounded by a finite set of formulae X L depending only on X and the logic L. Thus each system gives a nondeterministic decision procedure for the logic in question. The completeness proofs yield deterministic decision procedures for each logic because each proof is constructive. Each tableau system has a cut-free sequent analogue proving that Gentzen's cut-elimination theorem holds for these latter systems. The techniques are due to Hi...

. We describe here a general and flexible framework for decision making which embodies the concepts of beliefs, goals, options, arguments and commitments. We have employed these concepts to build a generic decision support system which has been successfully applied in a number of areas in clinical medicine. In this paper, we present the formalisation of the decision making architecture within a framework of modal propositional logics. A possible-world semantics of the logic is developed and the soundness and completeness result is also established. 1 Introduction A decision is a choice between two or more competing hypotheses about some world or possible courses of action in the world. A decision support system is a computerised system which helps decision makers by utilizing knowledge about the world to recommend beliefs or actions [1]. Such a system when built on symbolic theory [4] offers a general and flexible framework for decision making. The theory embodies the concepts of beli...

. We define cut-free display calculi for nominal tense logics extending the minimal nominal tense logic (MNTL) by addition of primitive axioms. To do so, we use a translation of MNTL into the minimal tense logic of inequality (MTL 6= ) which is known to be properly displayable by application of Kracht's results. The rules of the display calculus ffiMNTL for MNTL mimic those of the display calculus ffiMTL 6= for MTL 6= . Since ffiMNTL does not satisfy Belnap's condition (C8), we extend Wansing's strong normalisation theorem to get a similar theorem for any extension of ffiMNTL by addition of structural rules satisfying Belnap's conditions (C2)-(C7). Finally, we show a weak Sahlqvist-style theorem for extensions of MNTL, and by Kracht's techniques, deduce that these Sahlqvist extensions of ffiMNTL also admit cut-free display calculi. 1 Introduction Background: The addition of names (also called nominals) to modal logics has been investigated recently with different motivations; see...

this paper is to construct a similar correspondence between intermediate logics enriched with modal operators---we call them intuitionistic modal logics---and classical polymodal logics. That the Godel translation can be extended to an embedding of at least a few particular intuitionistic modal systems into some classical polymodal logics was observed by several authors (cf. [13], [25], [26], [5]). Fischer Servi [13], [15] used a variant of the translation to define "true" intuitionistic analogues of a number of classical modal systems. In [27] we exploited the translation proposed by Shehtman [25] to embed intuitionistic modal logics with the single necessity operator 2 of K into bimodal logics The work of the second authorwas supportedby the Alexandervon Humboldt Foundation. 1

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Abstract. We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework. 1 Three mistakes Pure Mathematics is the class of all propositions of the form ‘p implies q’... And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member... [45, p.3]. Thus begins the precursor of Principia Mathematica, Russell’s Principles of Mathematics, and thus begins the sad and confusing twentieth century tale of implication.

This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.

Abstract. Standard syntactic assignments (SSAs) model knowledge directly rather than as truth in all possible worlds as in modal epistemic logic, by assigning arbitrary truth values to atomic epistemic formulae. It is a very general approach to epistemic logic, but has no interesting logical properties — partly because the standard logical language is too weak to express properties of such structures. In this paper we extend the logical language with a new operator used to represent the proposition that an agent “knows at most ” a given finite set of formulae and study the problem of strongly complete axiomatization of SSAs in this language. Since the logic is not semantically compact, a strongly complete finitary axiomatization is impossible. Instead we present, first, a strongly complete infinitary system, and, second, a strongly complete finitary system for a slightly weaker variant of the language. 1