Inquisitive logic

Inquisitive Semantics gives rise to a combined logic of information and issues.

Inquisitive Logic is a non-substitution closed intermediate logic, which may be characterized as the fragment of intuitionistic logic consisting of disjunctions of negations. Roughly speaking, negations express classical declarative meanings, while disjunctions of them express issues.

For a detailed investigation of the features of this logic, an axiomatization of it, and its relations to important intermediate logics, such as the Kreisel-Putnam and the Medvedev logic, see my MSc thesis and my JPL paper with Floris Roelofsen.

Intermediate logics

Starting from Inquisitive Logic, I have looked at the effect of expanding an intermediate logic with the assumptions that the atoms are classical, that is, equivalent to their double negation. For what logics does this give rise to new schematic validities?
For some results on this, see chapter 5 of my MSc thesis.

Dichotomous inquisitive logic

More recently, I have looked at the logic of a variant of inquisitive semantics which, instead of assigning issue-raising potential to disjunction, extends the language with a syntactic category of interrogatives.

While closely related to standard inquisitive logic, this logic is a conservative extension of classical logic. This system is especially interesting since its notion of entailment encompasses as particular cases four crucial notions, namely, standard declarative entailment, answerhood, question presupposition, and interrogative entailment.

For this work, see my Synthese paper with Jeroen Groenendijk and Floris Roelofsen.

Inquisitive epistemic logic

Epistemic logic allows us to model and reason about situations consisting of certain facts together with what certain agents know about these facts, and about one another’s knowledge.

In modeling information exchange, it is important to keep track not only of the information agents have, but also of the information they want to obtain, that is, of the issues that they entertain.

Building on the uniform account of information and issues made available by inquisitive semantics, inquisitive epistemic logic gives us a natural but powerful conservative extension of EL, in which we can model and reason about situations consisting of facts, information and issues.

The logical language of IEL comprises declaratives and interrogatives, and it enables us to talk about issues that agents wonder about or know an answer to, as well as about issues that are publicly settled or publicly open in the exchange.

For more information, see the Synthese paper with Floris Roelofsen.

IDEL

Inquisitive dynamic epistemic logic is the dynamic version of inquisitive epistemic logic.

In standard DEL, public announcements establish new common knowledge. In IDEL, one may announce both declarative and interrogative sentences, and announcements may both establish new common knowledge, or raise new public issues.

For more information, see the Synthese paper with Floris Roelofsen.

NB: I am currently writing up an axiomatization result for the logic arising from both IEL and IDEL. I hope to make a draft available soon.