We present a modal extension of classical propositional logic in which intuitionistic propositional logic is mirrored by means of the modal operator. In this sense, the modal extension combines classical and intuitionistic propositional logic avoiding the collapsing problem. Adopting ideas from a recent paper (S. Lewitzka, A denotational semantics for a Lewis-style modal system close to S1, 201...

In this paper, we give some elements about agent-oriented relevance. For that, we define a new modal operator R a so that R a φ means that φ is relevant for agent a concerning the request Q. We discuss properties of this new operator, as well as its extensions and limits.

Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.

In this paper we present BTC, which is a logic for branching-time whose modal operator quantifies over histories and temporal operators involves a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL expresses an unrestricted quantification over histories and moments. The value of...

R. Meyer and E. Mares [10] studied the logic CNR, a classical relevant logic with a modal connective. Such logic is of type S4. As it has been noted in [10], the addition of a modal operator in the language of classical relevant logic and the axioms φ ∧ ψ → (φ ∧ ψ) and (φ ∧ ψ) → ( φ ∧ ψ) do not necessarily produce theorems such that as (φ→ ψ) → φ → ψ or (♦φ→ ψ) → (φ→ ψ). These formulas are well...

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is clos...

We describe the design of a collaborative cross-modal tool that supports visually-impaired and sighted coworkers to access and edit shared diagrams in real time and a case study of its use in a real world workplace environment. Our findings highlight the potential of cross-modal collaboration to improve workplace inclusion and identify initial challenges and opportunities for cross-modal design.

This paper presents CO3L, a compact, expressive and easy to use language for ontology representation. CO3L reflects the O3F model of ontology representation proposed elsewhere. The proposed language enables the representation of basic ontological entities, their relationships, and arbitrary axioms of the domain. Ontological entities include classes, properties, methods, facets and types. Relati...

R. M. Smullyan wrote in his book about islands, knights and knaves. The knights always tell the truth and the knaves are always lying. Instead of say we shall examine the can say modal operator. We show the soundness and the completeness of this logic.