•  18
    Logic of informal provability with truth values
    Logic Journal of the IGPL 31 (1): 172-193. 2023.
    Classical logic of formal provability includes Löb’s theorem, but not reflection. In contrast, intuitions about the inferential behavior of informal provability (in informal mathematics) seem to invalidate Löb’s theorem and validate reflection (after all, the intuition is, whatever mathematicians prove holds!). We employ a non-deterministic many-valued semantics and develop a modal logic T-BAT of an informal provability operator, which indeed does validate reflection and invalidates Löb’s theore…Read more
  •  16
    BAT is a logic built to capture the inferential behavior of informal provability. Ultimately, the logic is meant to be used in an arithmetical setting. To reach this stage it has to be extended to a first-order version. In this paper we provide such an extension. We do so by constructing non-deterministic three-valued models that interpret quantifiers as some sorts of infinite disjunctions and conjunctions. We also elaborate on the semantical properties of the first-order system and consider a c…Read more
  •  15
    Proof systems for BAT consequence relations
    Logic Journal of the IGPL 26 (1): 96-108. 2018.
  •  10
    The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.
  •  9
    Informal provability and dialetheism
    Theoria 89 (2): 204-215. 2023.
    According to the dialetheist argument from the inconsistency of informal mathematics, the informal version of the Gödelian argument leads us to a true contradiction. On one hand, the dialetheist argues, we can prove that there is a mathematical claim that is neither provable nor refutable in informal mathematics. On the other, the proof of its unprovability is given in informal mathematics and proves that very sentence. We argue that the argument fails, because it relies on the unjustified and u…Read more
  •  6
    Non-deterministic Logic of Informal Provability has no Finite Characterization
    Journal of Logic, Language and Information 30 (4): 805-817. 2021.
    Recently, in an ongoing debate about informal provability, non-deterministic logics of informal provability BAT and CABAT were developed to model the notion. CABAT logic is defined as an extension of BAT logics and itself does not have independent and decent semantics. The aim of the paper is to show that, semantically speaking, both logics are rather complex and they can be characterized by neither finitely many valued deterministic semantics nor possible word semantics including neighbourhood …Read more
  •  3
    8 Valued Non-Deterministic Semantics for Modal Logics
    with Daniel Skurt
    Journal of Philosophical Logic 1-21. forthcoming.
    The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic _K_. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these t…Read more
  •  1
    Rigor and formalization
    Synthese 203 (3): 1-18. 2024.
    This paper critically examines and evaluates Yacin Hamami’s reconstruction of the standard view of mathematical rigor. We will argue that the reconstruction offered by Hamami is premised on a strong and controversial epistemological thesis and a strong and controversial thesis in the philosophy of mind. Secondly, we will argue that Hamami’s reconstruction of the standard view robs it of its original philosophical rationale, i.e. making sense of the notion of rigor in mathematical practice.
  • Logics of Provability
    In Sven Ove Hansson & Vincent F. Hendricks (eds.), Introduction to Formal Philosophy, Springer. pp. 191-237. 2012.
    Provability logics are, roughly speaking, modal logics meant to capture the formal principles of various provability operators or predicates.