4 found
Order:
See also
Bruno Bentzen
Czech Academy of Sciences
  1.  29
    What Types Should Not Be.Bruno Bentzen - 2020 - Philosophia Mathematica 28 (1):60-76.
    In a series of papers Ladyman and Presnell raise an interesting challenge of providing a pre-mathematical justification for homotopy type theory. In response, they propose what they claim to be an informal semantics for homotopy type theory where types and terms are regarded as mathematical concepts. The aim of this paper is to raise some issues which need to be resolved for the successful development of their types-as-concepts interpretation.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  2. A Henkin-Style Completeness Proof for the Modal Logic S5.Bruno Bentzen - 2021 - In Pietro Baroni, Christoph Benzmüller & Yì N. Wáng (eds.), Logic and Argumentation: Fourth International Conference, CLAR 2021, Hangzhou, China, October 20–22. Springer. pp. 459-467.
    This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive logical (...)
    Download  
     
    Export citation  
     
    Bookmark  
  3.  58
    Frege on Referentiality and Julius Caesar in Grundgesetze Section 10.Bruno Bentzen - 2019 - Notre Dame Journal of Formal Logic 60 (4):617-637.
    This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It (...)
    Download  
     
    Export citation  
     
    Bookmark  
  4.  38
    Sense, Reference, and Computation.Bruno Bentzen - 2020 - Perspectiva Filosófica 47 (2):179-203.
    In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program–value analysis of sense and reference proposed by Martin-Löf building on previous work of Dummett. I propose a computational identity criterion for senses and argue that it validates what I see as the most plausible interpretation of Frege's equipollence principle for both sentences and singular terms. Before doing so, I examine Frege's implementation of his (...)
    Download  
     
    Export citation  
     
    Bookmark