Inquisitive modal logic, INQML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, INQML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in ...

While ∧,∨,¬ form a complete set of connectives for classical propositional logic, this does not hold for Łukasiewicz’s three-valued propositional logic, nor its generalization to n-valued logic. We define a unary connective r so that ∧,∨,¬, r form a complete set of connectives for n-valued Łukasiewicz logic. We discuss generalizations of this to infinitary logics. If we allow infinite conjuncti...

In this article we first show how the functional and the optimized functional translation from modal logic to many-sorted first-order logic can be naturally extended to the hybrid language H(@, ↓). The translation is correct not only when reasoning over the class of all models, but for any firstorder definable class. We then show that sorts can be safely removed (i.e., without affecting the sat...

The practical significance of the problem of combining logics is widely recognized, namely in knowledge representation (within artificial intelligence) and in formal specification and verification of algorithms and protocols (within software engineering and security). In these fields, the need for working with several calculi at the same time is the rule rather than the exception. For instance,...

Abstract We present a natural standard translation of inquisitive modal logic $\mathrm{InqML}$ into first-order over the two-sorted relational representations intended models, which captures built-in higher-order features . This is based on graded notion flatness that ties inherent second-order, team-semantic information states to subsets or tuples bounded size. A pseudo-models, relaxes non-ele...

The aim of the present paper is to discuss two different approaches for formulating independence friendly (IF) modal logic. In one of them, the language of basic modal logic is enriched with the slash notation familiar from IF first-order logics, and the resulting logic is interpreted in terms of games and uniform strategies. A different approach is formulated in the present paper: an IF modal ...

While propositional modal logic is a standard tool, first-order modal logic is not. Indeed, it is not generally understood that conventional first-order syntax is insufficiently expressible. In this paper we sketch a natural syntax and semantics for first-order modal logic, and show how it easily copes with well-known problems. And we provide formal tableau proof rules to go with the semantics,...

We present a logic, called fuzzy attribute logic, for reasoning about formulas describing particular attribute dependencies. The formulas are of a form A ⇒ B where A and B are collections of attributes. Our formulas can be interpreted in two ways. First, in data tables with entries containing degrees to which objects (table rows) have attributes (table columns). Second, in database tables where...