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. AguzzoliPrimo
;M. BianchiSecondo
;D. ValotaUltimo
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.File | Dimensione | Formato | |
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