Social choice and welfare economics are subjects at the frontier of many disciplines. Even if economics played the major rôle in their development, sociology, psychology and, principally, political science, mathematics and philosophy have been central for the manifold inventiveness of the employed methods and for the diversity of the studied topics. This phenomenon can be compared with game the...

In this paper we use the Kripke semantics characterization of Dummett logic to introduce a new way of handling non-forced formulas in tableau proof systems. We pursue the aim of reducing the search space by strictly increasing the number of forced propositional variables after the application of noninvertible rules. The focus of the paper is on a new tableau system for Dummett logic, for which ...

In this paper we use the Kripke semantics characterization of Dummett logic to introduce a new way of handling non-forced formulas in tableau proof systems. We pursue the aim of reducing the search space by strictly increasing the number of forced propositional variables after the application of non-invertible rules. The focus of the paper is on a new tableau system for Dummett logic, for which...

Gödel-Dummett logic is an extension of first-order intuitionistic logic with the linearity axiom (A ⊃ B)∨ (B ⊃ A), and the so-called “quantifier shift” axiom ∀x(A ∨ B(x)) ⊃ A ∨ ∀xB(x). Semantically, it can be characterised as a logic for linear Kripke frames with constant domains. Gödel-Dummett logic has a natural formalisation in hypersequent calculus. However, if one drops the quantifier shif...

Let Gm be the m-valued Gödel-Dummett fuzzy logic. If m ≥ 3 then neither conjunction nor implication is in Gm expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values. Gödel-Dummett fuzzy propositional logic can be defined as an extension of the intuitionistic propositional logic by th...