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2 Fundamenta Informaticae

2 2018

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Sequence Semantics for Modelling Reason-based Preferences

Calardo E., Governatori G., Rotolo A.

Fundamenta Informaticae

2018

Vol. 158, nr 1/3

217--238

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.

Logics for Modelling Collective Attitudes

Porello D.

Fundamenta Informaticae

2018

Vol. 158, nr 1/3

239--275

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained.