In the framework of t-norm based logics, Godel propositional logic G and drastic product logic DP are strictly connected. In this paper we explore the even stricter relation between DP and the logic G(Delta), the expansion of G with Baaz-Monteiro connective Delta. In particular we provide functional representations of free algebras in the corresponding algebraic semantics. We use then these functional representations to develop a theory of states, that is, finitely additive probability measures, for both G(Delta) and DP. Finally, we use dual equivalences for the algebraic semantics of both G(Delta) and DP, to provide a completely combinatorial characterization of states.

Free algebras, states and duality for the propositional GödelΔ and Drastic Product logics / S. Aguzzoli, M. Bianchi, B. Gerla, D. Valota. - In: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING. - ISSN 0888-613X. - 104(2019 Jan), pp. 57-74.

Free algebras, states and duality for the propositional GödelΔ and Drastic Product logics

S. Aguzzoli
Primo
;
M. Bianchi
Secondo
;
D. Valota
Ultimo
2019

Abstract

In the framework of t-norm based logics, Godel propositional logic G and drastic product logic DP are strictly connected. In this paper we explore the even stricter relation between DP and the logic G(Delta), the expansion of G with Baaz-Monteiro connective Delta. In particular we provide functional representations of free algebras in the corresponding algebraic semantics. We use then these functional representations to develop a theory of states, that is, finitely additive probability measures, for both G(Delta) and DP. Finally, we use dual equivalences for the algebraic semantics of both G(Delta) and DP, to provide a completely combinatorial characterization of states.
Probability measures in non-classical logics; Godel propositional logic; Godel(Delta) propositional logic; Drastic Product logic; Free algebras
Settore MAT/01 - Logica Matematica
Settore INF/01 - Informatica
gen-2019
1-nov-2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/598695
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