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.

Semisimplicity, EDPC and Discriminator Varieties of Bounded Weak-commutative Residuated Lattices with an S4-like Modal Operator

Abstract: In this paper, we show that all semisimple varieties of bounded weak-commutative residuated lattices with an S4-like modal operator are discriminator varieties. We also give a characterization of discriminator and EDPC varieties of bounded weak-commutative residuated lattices with an S4-like modal operator follows.

Setting the Basis for Here and There Modal Logics.

Abstract: We define and study a new modal extension of the logic of Here and There with operators from modal logic K. We provide a complete axiomatisation together with several results such as the non-interdefinability of modal operators, the Hennessy-Milner and the finite model properties, a bound for the complexity of the related satisfiability problem and a discussion about the canonicity of some well-known Sahlqvist formulas in our setting. We also consider the equilibrium property on this logic and we prove the theorem of strong equivalence in the resulting framework.

Zirkumstantielle Modalität im Bairischen: das verbale Präfix der-

Abstract: Drawing on the results of a questionnaire administered in the region between and around Altotting and Trostberg in south-eastern Bavaria, this contribution focuses on the Bavarian verbal prefix der-, particularly on its syntactic and semantic characteristics. The investigation reveals that a distinction needs to be drawn between a specifically Bavarian use of der- and one that corresponds to the Standard German usage of the prefix. In syntactic terms, the specifically Bavarian der- is characterized by its need for a direct object and an agentive, intentional subject; semantically it can be described as a narrow, goal-directed path. The characteristic modal affinity of verbs which take the der- prefix can be attributed to the interaction of these traits. This affinity is apparent not just in the frequent combination of der- verbs with konnen, but also in the modal interpretation of such verbs, possible even in the absence of a modal operator. The modal interpretation of derverbs is, however, confined to a particular form of dynamic modality - namely circumstantial modality, i.e., the ability, within specific circumstances, of a subject to successfully execute a deed or action up to a defined end point.

Chapter Seven. Modal Logic And Possible Worlds

Abstract: Seventeenth-century discussions on divine knowledge and will thoroughly employ modal categories like contingency and necessity. In fact, the major systematic positions can be distinguished by the way they relate modal aspects to divine agency. Since the early twentieth century, important developments have been achieved in the study of modal logic, enabling us to analyze the involved modal issues more exactly. In this chapter, these tools are introduced to evaluate the seventeenth-century positions and to develop a contemporary analysis of divine agency that takes account of its modal aspects. Modern modal logic with its symbolic language and possible world semantics delivers a framework to evaluate the various seventeenth- century conceptions of divine agency, which all have a clear modal structure.Keywords: divine knowledge; modal logic

Denotational Semantics for interrogative Sentences in Japanese

Abstract: We present a new approach to a sentence of interrogative form in Japanese within the framework of Montague Grammar. The possibility of various uses of an interrogative sentence; uses as a question, an exclamation, a rhetorical question, a demand and a recommendation is explained based on the same denotation for the sentence. The denotation which is neutral for all possible uses is defined in terms of a new modal operator in the formal language level, and of possible world semantics in the denotational level. Our interpretation of the" Japanese end marker particle "ka" also explains some other usages of the same particle "ka" in a uniform way; especially, "ka" as the parallel listing (disjunctive) particle, which is another important usage of "ka", is explained uniformly with the interrogative "ka". This uniform interpretation in the denotational semantics level will be supported by the historical development of usages of "ka", as briefly explained. Some part of our new approach for the Japanese interrogative forms can be, in our opinion, generalized to many other languages, although there are also some part particular to Japanese.