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  1. Matteo Bianchi (2013). First-Order Nilpotent Minimum Logics: First Steps. Archive for Mathematical Logic 52 (3-4):295-316.
    Inspired by the work done by Baaz et al. (Ann Pure Appl Log 147(1–2): 23–47, 2007; Lecture Notes in Computer Science, vol 4790/2007, pp 77–91, 2007) for first-order Gödel logics, we investigate Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra, establishing also a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, undecidability and (...)
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  2. Matteo Bianchi (2013). The Variety Generated by All the Ordinal Sums of Perfect MV-Chains. Studia Logica 101 (1):11-29.
    We present the logic BLChang, an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BLChang-algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new (...)
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  3. Matteo Bianchi & Franco Montagna (2011). N-Contractive BL-Logics. Archive for Mathematical Logic 50 (3-4):257-285.
    In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom ${\phi^n\rightarrow\phi^{n+1}}$ , for some ${n\in\mathbb{N}^+}$ ) axiomatic extensions of BL and their corresponding varieties: BL n , SBL n , BL n and SBL n . Concerning BL n we have that every BL n -chain is isomorphic to an (...)
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  4. Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra (2009). A Temporal Semantics for Basic Logic. Studia Logica 92 (2):147 - 162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  5. Matteo Bianchi & Franco Montagna (2009). Supersound Many-Valued Logics and Dedekind-MacNeille Completions. Archive for Mathematical Logic 48 (8):719-736.
    In Hájek et al. (J Symb Logic 65(2):669–682, 2000) the authors introduce the concept of supersound logic, proving that first-order Gödel logic enjoys this property, whilst first-order Łukasiewicz and product logics do not; in Hájek and Shepherdson (Ann Pure Appl Logic 109(1–2):65–69, 2001) this result is improved showing that, among the logics given by continuous t-norms, Gödel logic is the only one that is supersound. In this paper we will generalize the previous results. Two conditions will be presented: the first (...)
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