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.

Agency and fictional truth: a formal study on fiction-making

Abstract: Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language $$\mathcal {L}$$ of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of $$\mathcal {L}$$ with respect to other modal languages is a variety of operators having to do with fictional truth, including a ‘fictionality’ operator $$M $$ (to be read as “it is a fictional truth that”). Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for.

Optimization of Bounded Model Checking

Abstract: This paper optimizes the encoding of verifying G(p) and G(p→F(q)) which are two important and frequently used modal operators in optimization of encoding for bounded model checking (BMC). Through analysis of the properties of finite state machine (FSM) and LTL (linear-time temporal logic) when verifying these modal operators, it presents a concise recursive formula, which can efficiently translate BMC instances into SAT (satisfiability) instances. The logical properties of these recursion formulas are verified. The experimental comparison between the optimization of BMC and the other two important methods AA_BMC and Timo_BMC for solving these modal operators in BMC shows that the former is superior to the latter in both the scale of instances and the difficulty to solve the problem. Research of this paper is also beneficial to encoding optimization of verifying other modal operators in BMC.

A Study of Subminimal Logics of Negation and Their Modal Companions

Abstract: We study propositional logical systems arising from the language of Johansson’s minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use duality and completeness results to show that there are uncountably many subminimal logics. We also give model-theoretic and algebraic definitions of filtration for minimal logic and show that they are dual to each other. These constructions ensure that the propositional minimal logic has the finite model property. Finally, we define and investigate bi-modal companions with non-normal modal operators for some relevant subminimal systems, and give infinite axiomatizations for these bi-modal companions.