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.

Monotonic Distributive Semilattices

Abstract: In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.

Axiomatizations of intuitionistic double negation

Abstract: We investigate intuitionistic propositional modal logics in which a modal operator is equivalent to intuitionistic double negation. Whereas ¬¬ is divisible into two negations, is a single indivisible operator. We shall first consider an axiomatization of the Heyting propositional calculus H, with the connectives →,∧,∨ and ¬, extended with . This system will be called Hdn (“dn” stands for “double negation”). Next, we shall consider an axiomatization of the fragment of H without ¬ extended with . This system will be called Hdn. We shall show that these systems are sound and complete with respect to specific classes of Kripke-style models with two accessibility relations, one intuitionistic and the other modal. This type of models is investigated in [2] and [3], and here we try to apply the techniques of these papers to an intuitionistic modal operator with a natural interpretation. The full results of our investigation will be published in [4] and [1].

Knowlog: a declarative language for reasoning about knowledge in distributed systems

Abstract: In the last few years, researchers started to investigate how recursive queries and deductive languages can be applied to find solutions to the new emerging trends in distributed computing. We conjecture that a missing piece in the current state-of-the-art in logic programming is the capability to express statements about the knowledge state of distributed nodes. In fact, reasoning about the state of remote nodes is fundamental in distributed contexts in order to design and analyze protocols behavior. To reach this goal, we leveraged Datalog¬ with an epistemic modal operator, allowing the programmer to directly express nodes' state of knowledge instead of low level communication details. To support the effectiveness of our proposal, we introduce, as example, the declarative implementation of the two phase commit protocol.

W-JS: a modal logic of knowledge

Abstract: W-JS is a first-order predicate calculus on the modal theory of knowledge. It is based on natural deduction rules and accompanied by possible-world-accessibility semantics. As an example, the famous "Mr. S and Mr. P" puzzle is solved in W-JS.