## 65 Citations

Stoic Sequent Logic and Proof Theory

- PhilosophyHistory and Philosophy of Logic
- 2019

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is…

A New Representation Theorem for Many-valued Modal Logics

- Computer Science, MathematicsArXiv
- 2011

We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and…

Autoreferential semantics for many-valued modal logics

- Mathematics, Computer ScienceJ. Appl. Non Class. Logics
- 2008

The autoreferential Kripke-style semantics for this class of modal algebras is based on the set of possible worlds equal to the complete lattice of algebraic truth-values, while all intermediate possible worlds represent the different levels of paraconsistent logics.

Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen

- Computer Science, MathematicsBulletin of Symbolic Logic
- 2002

It is shown that Paul Hertz anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory.

Semantic Values for Natural Deduction Derivations

- Mathematics, Computer ScienceSynthese
- 2004

Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between…

The Consistency of Arithmetic

- The Australasian Journal of Logic
- 2021

This paper offers an elementary proof that formal arithmetic is consistent. The system that will be proved consistent is a first-order theory R♯, based as usual on the Peano postulates and the…

The Deduction Theorem ( before and after Herbrand ) C

- 2021

Attempts to articulate the real meaning or ultimate significance of a famous theorem comprise a major vein of philosophical writing about mathematics. The subfield of mathematical logic has supplied…

Metalogic, Schopenhauer and Universal Logic

- Philosophy
- 2020

Schopenhauer used the word “metalogical” since his first work, On the Fourfold Root of the Principle of Sufficient Reason (1813), being the first to give it a precise meaning and a proper place…

The Explosion Calculus

- Computer Science, MathematicsStud Logica
- 2020

A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules that explode a given sequent into its elementary structural sequents, which do not contain any logical constants.

Analyticity, Balance and Non-admissibility of $$\varvec{Cut}$$Cut in Stoic Logic

- Mathematics, Computer ScienceStud Logica
- 2019

This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion.