A Multi-type Calculus for Inquisitive Logic. In International Workshop on Logic, Language, Information, and Computation, pages 215–233. Springer. abstract bibtex In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework developed by Groenendijk, Roelofsen and Ciardelli which captures both assertions and questions in natural language. Inquisitive logic adopts the so-called support semantics (also known as team semantics). The Hilbert-style presentation of inquisitive logic is not closed under uniform substitution, and some axioms are sound only for a certain subclass of formulas, called flat formulas. This and other features make the quest for analytic calculi for this logic not straightforward. We develop a certain algebraic and order-theoretic analysis of the team semantics, which provides the guidelines for the design of a multi-type environment accounting for two domains of interpretation, for flat and for general formulas, as well as for their interaction. This multi-type environment in its turn provides the semantic environment for the multi-type calculus for inquisitive logic we introduce in this paper.
Downloads: 0
{"_id":"nBrnHy5QKHZxP4vKE","bibbaseid":"anonymous-amultitypecalculusforinquisitivelogic","bibdata":{"bibtype":"inproceedings","type":"inproceedings","author":[{"propositions":[],"lastnames":["Frittella"],"firstnames":["Sabine"],"suffixes":[]},{"propositions":[],"lastnames":["Greco"],"firstnames":["Giuseppe"],"suffixes":[]},{"propositions":[],"lastnames":["Palmigiano"],"firstnames":["Alessandra"],"suffixes":[]},{"propositions":[],"lastnames":["Yang"],"firstnames":["Fan"],"suffixes":[]}],"booktitle":"International Workshop on Logic, Language, Information, and Computation","organization":"Springer","pages":"215–233","keywords":"inquisitive logic","title":"A Multi-type Calculus for Inquisitive Logic","abstract":"In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework developed by Groenendijk, Roelofsen and Ciardelli which captures both assertions and questions in natural language. Inquisitive logic adopts the so-called support semantics (also known as team semantics). The Hilbert-style presentation of inquisitive logic is not closed under uniform substitution, and some axioms are sound only for a certain subclass of formulas, called flat formulas. This and other features make the quest for analytic calculi for this logic not straightforward. We develop a certain algebraic and order-theoretic analysis of the team semantics, which provides the guidelines for the design of a multi-type environment accounting for two domains of interpretation, for flat and for general formulas, as well as for their interaction. This multi-type environment in its turn provides the semantic environment for the multi-type calculus for inquisitive logic we introduce in this paper.","key":"Frittella:16","id":"Frittella:16","bibbaseid":"anonymous-amultitypecalculusforinquisitivelogic","role":"author","urls":{},"keyword":["inquisitive logic"],"metadata":{"authorlinks":{}}},"bibtype":"inproceedings","biburl":"https://projects.illc.uva.nl/inquisitivesemantics/assets/files/papers.bib","dataSources":["LaLDs2mrYhQpgH6Lk"],"keywords":["inquisitive logic"],"search_terms":["multi","type","calculus","inquisitive","logic"],"title":"A Multi-type Calculus for Inquisitive Logic","year":null}