TY - GEN
T1 - A multi-type calculus for inquisitive logic
AU - Frittella, Sabine
AU - Greco, Giuseppe
AU - Palmigiano, Alessandra
AU - Yang, Fan
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-662-52921-8_14
DO - 10.1007/978-3-662-52921-8_14
M3 - Conference contribution
AN - SCOPUS:84981501522
SN - 9783662529201
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 215
EP - 233
BT - Logic, Language, Information, and Computation - 23rd International Workshop, WoLLIC 2016, Proceedings
A2 - Väänänen, Jouko
A2 - Hirvonen, Åsa
A2 - de Queiroz, Ruy
PB - Springer Verlag
T2 - 23rd International Workshop on Logic, Language, Information, and Computation, WoLLIC 2016
Y2 - 16 August 2016 through 19 August 2016
ER -