Topic
Modal operator
About: Modal operator is a research topic. Over the lifetime, 1151 publications have been published within this topic receiving 22865 citations. The topic is also known as: modal connective.
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26 Jun 2008
TL;DR: The authors investigated the aspectual and modal marking in Japanese verbal complex, and as a result offered support for the hypothesis of a link between aspect and deontic vs. epistemic interpretation of modal markers.
Abstract: This contribution investigates the aspectual and modal marking in the Japanese verbal complex, and as a result offers support for the hypothesis of a link between aspect and deontic vs. epistemic interpretation of modal markers. Since Japanese is structurally largely different from the Germanic and the Slavic languages and is genetically unrelated, the aspect-modality link must be motivated by general cognitive principles. On the other hand, I suggest that with respect to some points in Abraham’s and Leiss’s (in this volume) theory of the aspect-modality link a revision might be called for. Concretely, I propose the following: (1) The temporality of deontic modal sentences differs from epistemic modal sentences in that deontic modal sentences require [S ≠ E] (E standing for the event time in the complement) while there are no such restrictions on sentences with epistemic modals. (2) The crucial factor in modal interpretation is temporal rather than aspectual. Aspectuality mediates between modality and temporality rather than motivating or entailing modality directly. (3) Grammatical aspect only provides a cue to modal interpretation, but cannot determine it. The ultimate determining factor is context, which provides either a volitive or non-volitive background to the utterance.
2 citations
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13 Jul 2000TL;DR: The paper adds the /spl rarr/ connective to Layman's probability theory, provides this with the well-known Lukasiewicz interpretation, and explores its properties with respect to the system as a whole.
Abstract: A prior work introduced Layman's probability theory as a formal system for reasoning with linguistic likelihood, wherein the logical and is interpreted as the arithmetic min, and the or is interpreted as the max. Likelihood modifiers (likely, very likely, somewhat unlikely, etc.) are treated as modal operators. The system is two-leveled, with the lower level being a multivalent logic and the upper level being bivalent. In the previous treatment, the lower level employed only the connectives V, /spl and/, and /spl sim/. The paper adds the /spl rarr/ connective, provides this with the well-known Lukasiewicz interpretation, and explores its properties with respect to the system as a whole.
2 citations
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TL;DR: This paper introduces a Gentzen-type sequent calculus SBIS for BIS, and the cut-elimination and decidability theorems for SBIS are proved and the completeness theorem with respect to this semantics is proved.
2 citations
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01 Jan 1993
TL;DR: In this article, a modal operator square is used to express the belief of an agent in terms of possible worlds using the modal logic KD45, where the belief operator can be interpreted in the context of a world agent is acting in and the agent's beliefs about the world and its beliefs about other agents' beliefs.
Abstract: In multi-agent systems a group of autonomous intelligent systems, called agents, acts and cooperates in a world in order to achieve certain goals Such systems are in general assumed to have no central control structure and hence each agent can only perform actions that are based on his local knowledge and on his local beliefs In the literature knowledge of agents is mostly represented under the view that knowledge is true belief On the other hand, if agents are acting in a (real) world their knowledge often is obtained by perception and communication, and hence typically is not true Thus, the use of belief - where agents may have false beliefs - seems more appropriate than the use of knowledge in multi-agent systems Terminological logics provide a well-investigated and decidable fragment of first-order logics that is much more expressive than propositional logic and well suited to describe a world agents are acting in However, knowledge or belief of agents can only be represented in a very limited way In this paper we investigate how terminological logics can be extended in such a way that belief of agents can be represented in an adequate manner We therefore exemplarily extend the concept language mathcal{ALC} by a modal operator square, which is indexed by agents Thereby, square_{i}varphi represents the fact "agent i believes varphi'; This belief operator will be interpreted in terms of possible worlds using the well-known modal logic KD45 This extended language mathcal{ALC_{B}} provides a uniform formalism to describe both, a world agents are acting in and the beliefs agents have about this world and about their own and other agents' beliefs Thus, it can be seen as a two-dimensional extension of mathcal{ALC} which allows both, reasoning about objective facts that hold in the world and reasoning on the level of possible worlds We will give sound and complete algorithms to check consistency of the represented beliefs and to decide whether an mathcal{ALC_{B}}-sentence is logically entailed by the beliefs of agents Hence, when acting in a world agents can use beliefs which are explicitly represented as well as implicit beliefs that are entailed by their knowledge base
2 citations
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TL;DR: Modal realists should fashion their theory by postulating and taking seriously the modal equivalent of tense, or modal tense This will give them a uniform way to respond to five different objections, one each by Skyrms, Quine, and Peacocke, and two by van Inwagen as mentioned in this paper.
Abstract: Modal realists should fashion their theory by postulating and taking seriously the modal equivalent of tense, or modal tense This will give them a uniform way to respond to five different objections, one each by Skyrms, Quine, and Peacocke, and two by van Inwagen, and suggest a non-Lewisian path to modal realism
2 citations