•  64
  •  57
    Naive Modus Ponens and Failure of Transitivity
    Journal of Philosophical Logic 45 (1): 65-72. 2016.
    In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I r…Read more
  •  27
    Logical Nihilism and the Logic of ‘prem’
    Logic and Logical Philosophy 1. forthcoming.
  •  19
    Non-classical Elegance for Sequent Calculus Enthusiasts
    Studia Logica 105 (1): 93-119. 2017.
    In this paper we develop what we can describe as a “dual two-sided” cut-free sequent calculus system for the non-classical logics of truth lp, k3, stt and a non-reflexive logic ts which is, arguably, more elegant than the three-sided sequent calculus developed by Ripley for the same logics. Its elegance stems from how it employs more or less the standard sequent calculus rules for the various connectives and truth, and the fact that it offers a rather neat connection between derivable sequents a…Read more
  •  17
    Structural proof theory for first-order weak Kleene logics
    Journal of Applied Non-Classical Logics 30 (3): 272-289. 2020.
    This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.
  •  17
    Herzberger’s Limit Rule with Labelled Sequent Calculus
    Studia Logica 108 (4): 815-855. 2020.
    Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the tw…Read more
  •  16
    Infinitary Contraction‐Free Revenge
    Thought: A Journal of Philosophy 7 (3): 179-189. 2018.
  •  15
    Omega-inconsistency without cuts and nonstandard models
    Australasian Journal of Logic 13 (5). 2016.
    This paper concerns the relationship between transitivity of entailment, omega-inconsistency and nonstandard models of arithmetic. First, it provides a cut-free sequent calculus for non-transitive logic of truth STT based on Robinson Arithmetic and shows that this logic is omega-inconsistent. It then identifies the conditions in McGee for an omega-inconsistent logic as quantified standard deontic logic, presents a cut-free labelled sequent calculus for quantified standard deontic logic based on …Read more
  •  11
    A note on the cut-elimination proof in “truth without contraction”
    Review of Symbolic Logic 13 (4): 882-886. 2020.
    This note shows that the permutation instructions presented by Zardini for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKTω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKTω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be sho…Read more