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.

Deciding modal logics using tableaux and set theory.

Abstract: We propose a tableau-like decision procedure for deciding the satisfiability of set-theoretical formulae with restricted universal quantifiers and the powerset operator. Our result apply to a rather large class of set theories. The procedure we define can be used as a subroutine to decide the same class of formulae both in Set Theory and in non well-founded set theories, since we assume neither Regularity nor any form of anti-foundation axiom. Moreover, the decidability result presented allow to characterize a class of decidable modal logics. Thanks to the 2-as-P (box-as-powerset) translation our procedure can be used to uniformly study a large class of modal logics which includes K, T , S4, S5, S4.3.

Godel's Property Abstraction Operator and Possibilism

Abstract: Godel’s Ontological Argument, the most sophisticated and formal of ontological arguments, relies heavily on the notion of positive property, which according to Godel, is a property “independent of the accidental structure of the world”; “pure attribution,” as opposed to privation; “positive in the moral aesthetic sense.” Pure attribution seems likely to be related to the Leibnizian concept of perfection. Godel’s Ontological Argument is even more distinctive because it employs a third-order modal logic with a property abstraction operator and property quantification into modal contexts. Godel presents his argument without ever presenting the details of the formal system of logic being employed. The omission is serious because without it the philosophical presuppositions are hard to assess. Furthermore, Godel never discussed an applied semantics to both explicate the modal operators and relate the formal representations in the argument to the intended meanings. In Godel’s Ontological Argument (2000), the formal syntax and semantics of third-order modal logic with property abstraction were constructed, and a completeness theorem for third order modal Logic with property abstraction for faithful models was proved. I argued that it was not possible to develop a sufficient applied third-order modal semantics for Godel’s ontological argument nor was it possible for

Computational Complexity of Core Fragments of Modal Logics T, K4, and S4

Abstract: We show that the satisfiability problem in core fragments of modal logics T, K4, and S4 in whose languages diamond modal operators are disallowed is NL-complete. Moreover, we provide deterministic procedures for satisfiability checking. We show that the above fragments correspond to certain core fragments of linear temporal logic, hence our results imply NL-completeness of the latter.

A Temporal Logic for Higher-Order Functional Programs

Abstract: We propose an extension of linear temporal logic that we call Linear Temporal Logic of Calls (LTLC) for describing temporal properties of higher-order functions, such as “the function calls its first argument before any call of the second argument.” A distinguishing feature of LTLC is a new modal operator, the call modality, that checks if the function specified by the operator is called in the current step and, if so, describes how the arguments are used in the subsequent computation. We demonstrate expressiveness of the logic, by giving examples of LTLC formulas describing interesting properties. Despite its high expressiveness, the model checking problem is decidable for deterministic programs with finite base types.

Situation event logic for early validation of multi-agent systems

Abstract: Nowadays agent-oriented software engineering methodologies emphasize the importance of the environment in which a multiagent system (MAS) operate. Meanwhile, they do not propose any diagram to represent the environment and its effects on the MAS. So, we propose two diagrams that can be introduced in agent-oriented methodologies: an environment diagram representing environment evolution over time, and an agent diagram showing the MAS organization according to the agents' roles and their relationships. Furthermore, many model checking techniques were defined to validate whether a MAS will solve the problem for which it is designed. However, these techniques do not consider the environment in their checking procedure. We propose a Situation Event Logic, an extension of modal logic, in which modal operators have a well defined scope over a set of situations. This logic is used to represent and infer knowledge from the environment and agent diagrams.