Affiliations: [a] CIRSFID, University of Bologna, Via Galliera 3, 40122 Bologna, Italy. erica.calardo@unibo.it | [b] Data61, CSIRO, 41 Boggo Road, Dutton Park, Queensland, 4109, Australia. guido.governatori@data61.csiro.au | [c] CIRSFID, University of Bologna, Via Galliera 3, 40122 Bologna, Italy. antonino.rotolo@unibo.it
Correspondence:
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Address for correspondence: Data61, CSIRO, 41 Boggo Road, Dutton Park, Queensland, 4109, Australia
Abstract: We study how the non-classical n-ary operator ⊗, originally intended to capture the concept of reparative obligation, can be used in the context of social choice theory to model preferences. A novel possible-world model-theoretic semantics, called sequence semantics, was proposed for the operator. In this paper, we propose a sound and complete axiomatisation of a minimal modal logic for the operator, and we extend it with axioms suitable to model social choice consistency principles such as extension consistency and contraction consistency. We provide completeness results for such extensions.
Keywords: Sequence semantics, preferences, modal logic, non normal modal logics, neighbourhood semantics, social choice theory, choice consistency
