No abstract

Neste artigo, eu revisito a teoria do sentido e referência de Frege no cenário construtivo das explicações de significado da teoria dos tipos, estendendo e aprimorando a análise em termos de programa-valor da teoria de sentido e referência proposta por Martin-Löf, baseada em trabalhos anteriores de Dummett. Eu proponho um critério de identidade computacional para senti-dos e defendo que ele valida o que considero a interpretação mais plausível do princípio de equipolência de Frege, tanto para sentenças quanto para ter-mos singulares. Antes de fazer isso, examino a implementação de Frege de sua teoria dos sentidos e referência no quadro lógico de Grundgesetze, sua doutrina dos valores da verdade, e sua interpretação de igualdade de sentido como equipolência de afirmações.

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 is argued that, in Frege's standards of reducing arithmetic to logic, his solution to the indeterminacy does not give rise to any sort of Caesar problem in the book.

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover [5]. The proof formalized is close to that of Hughes and Cresswell [11], 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 connectives and necessity as the only primitive modal operator. The full source code is available online at https: //github.com/bbentzen/mpl/ and has been typechecked with Lean 3.4.2.

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality.