7 found
  1.  29
    Two Kinds of Consequential Implication.Claudio E. A. Pizzi - 2018 - Studia Logica 106 (3):453-480.
    The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength and \). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for (...)
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  2.  14
    Possibility and Dyadic Contingency.Claudio E. A. Pizzi - 2022 - Journal of Logic, Language and Information 31 (3):451-463.
    The paper aims at developing the idea that the standard operator of noncontingency, usually symbolized by Δ, is a special case of a more general operator of dyadic noncontingency Δ(−, −). Such a notion may be modally defined in different ways. The one examined in the paper is __Δ__(B, A) = df ◊B ∧ (A ⥽ B ∨ A ⥽ ¬B), where ⥽ stands for strict implication. The operator of dyadic contingency __∇__(B, A) is defined as the negation of __Δ__(B, (...)
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  3.  21
    Axioms for a Logic of Consequential Counterfactuals.Claudio E. A. Pizzi - 2023 - Logic Journal of the IGPL 31 (5):907-925.
    The basis of the paper is a logic of analytical consequential implication, CI.0, which is known to be equivalent to the well-known modal system KT thanks to the definition A → B = df A ⥽ B ∧ Ξ (Α, Β), Ξ (Α, Β) being a symbol for what is called here Equimodality Property: (□A ≡ □B) ∧ (◊A ≡ ◊B). Extending CI.0 (=KT) with axioms and rules for the so-called circumstantial operator symbolized by *, one obtains a system CI.0*Eq (...)
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  4.  18
    Normatively determined propositions.Matteo Pascucci & Claudio E. A. Pizzi - 2022 - In V. Giardino, S. Linker, S. Burns, F. Bellucci, J. M. Boucheix & P. Viana (eds.), Diagrammatic Representation and Inference. Diagrams 2022. Springer. pp. 78-85.
    In the present work we provide a logical analysis of normatively determined and non-determined propositions. The normative status of these propositions depends on their relation with another proposition, here named reference proposition. Using a formal language that includes a monadic operator of obligation, we define eight dyadic operators that represent various notions of “being normatively (non-)determined”; then, we group them into two families, each forming an Aristotelian square of opposition. Finally, we show how the two resulting squares can be combined (...)
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  5. Permanence vs. termination: a logical analysis.Matteo Pascucci & Claudio E. A. Pizzi - 2022 - Logique Et Analyse 257:57-78.
    The present article is devoted to a logical inquiry on the notions of permanence and termination, which play a central role in many areas of temporal reasoning. In the first part, we introduce a bimodal framework to represent these notions and provide a syntactic and semantic comparison with a monomodal framework representing the notion of future necessity. In the second part, we focus on the problem of defining synonymous logical systems over the two frameworks; as an example, we provide an (...)
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  6.  19
    A Syntactical Analysis of Lewis’s Triviality Result.Claudio E. A. Pizzi - forthcoming - Logic and Logical Philosophy:1.
  7.  82
    Counterfactuals and the complexity of causal notions.Claudio Pizzi & Claudio E. A. Pizzi - 1990 - Topoi 9 (2):147-155.