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...

Density elimination by substitutions is introduced as a uniformmethod for removing applications of the Takeuti-Titani density rule from proofs in firstorder hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cut-elimination. Moreover, adding the density rule to any axiomatic extension of a simple first-order lo...

We address the problem of answering queries in circumscription and related nonmonotonic formalisms. The answering process we describe uses resolution-based theorem provers recently developed for circumscription. In a way analogous to query answering techniques in classical predicate logic, the process extracts information from a proof of the query. Circumscriptive theorem provers consist of two...

Possibilism is the position that it is possible to make a veridical statement about something, which doesn’t exist. Based on this observation, actualism and possibilism can be defined in first-order predicate logic by means of one or more existence predicates. It is argued that an analogous distinction can be made in the realm of first-order modal logic, and that this distinction ought to be ac...

We define a sound and complete logic, called FO⊃, which extends classical first-order predicate logic with intuitionistic implication. As expected, to allow the interpretation of intuitionistic implication, the semantics of FO⊃ is based on structures over a partially ordered set of worlds. In these structures, classical quantifiers and connectives (in particular, implication) are interpreted wi...