In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores...

We introduce various new supraclassical entailment relations for defeasible reasoning and investigate some of their relationships. The contrapositive of the usual nonmonotonic preferential entailment turns out to be a monotonic supraclassical entailment. Analogously to these two, a nonmonotonic and its contrapositive monotonic supraclassical entailment can be defined by using modal operators re...

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation τ(a) ≤ b ∨ (b → a), for all a, b ∈ A. These operators were studied from an algebraic, logical an...

A bilattice is a set equipped with two partial orders and a negation operation that inverts one of them while leaving the other unchanged; it has been suggested that the truth values used by inference systems should be chosen from such a structure instead of the two-point set {t, f}. Given such a choice, we redefine a modal operator to be a function on the bilattice selected, and show that this...

The paper considers the standard concept description language ALC augmented with various kinds of modal operators which can be applied to concepts and axioms. The main aim is to develop methods of proving decid-ability of the satissability problem for this language and apply them to description logics with most important temporal and epis-temic operators, thereby obtaining satissa-bility checki...

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form AG:xφ reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that φ’. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the...

In this paper, we construct a new concept description language intended for representing dynamic and intensional knowledge. The most important feature distinguishing this language from its predecessors in the literature is that it allows applications of modal operators to all kinds of syntactic terms: concepts, roles and formulas. Moreover, the language may contain both local (i.e., state-depen...

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessar...

In this paper, we consider the influence of trust on the assimilation of acquired information into an agent’s belief. By use of modal logic, we semantically and axiomatically characterize the relationship among belief, information acquisition and trust. The belief and information acquisition operators are respectively represented by KD45 and KD normal modalities, whereas trust is denoted by a m...

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simplemin...