Fregean logics with the multiterm deduction theorem and their algebraization

  title={Fregean logics with the multiterm deduction theorem and their algebraization},
  author={Janusz Czelakowski and Don Pigozzi},
  journal={Studia Logica},
AbstractA deductive system $$\mathcal{S}$$ (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas $$\{ \left\langle {\alpha ,\beta } \right\rangle :T,\alpha \vdash s \beta and T,\beta \vdash s \alpha \} ,$$ is a congruence relation on the formula algebra. The multiterm deduction-detachment theorem is a natural generalization of the deduction theorem of the classical and intuitionistic propositional… 

Categorical Abstract Algebraic Logic: Selfextensional …-Institutions with Implication

The work of Jansana on selfextensional deductive systems with an implication satisfying the deduction-detachment property, that was partially based on the well-known work of Font and Jansana on

Fregean logics


  • T. Moraschini
  • Philosophy, Mathematics
    The Review of Symbolic Logic
  • 2018
It is shown that the fact that the truth sets of $Mo{d^{\rm{*}}}{\cal L}$ can be defined by means of equations with universally quantified parameters is captured by an order-theoretic property of the Leibniz operator restricted to deductive filters of ${\ cal L}$.

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The analysis of unital systems leads to the concept of Lindenbaum–Tarski algebra which, under some natural conditions, is a free algebra in a variety closely related to the deductive system in focus.

Deduction-detachment theorem in hidden k-logics

A syntactic notion of translation is introduced, which will be used to define an equivalence relation between hidden k-logics, and it is shown that this notion of equivalence preserves some logical properties, namely the deduction-detachment theorem (DDT) and the Craig interpolation property.

Generalized Matrices in Abstract Algebraic Logic

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Beyond Rasiowa's Algebraic Approach to Non-classical Logics

The impact of Rasiowa's well-known book on the evolution of algebraic logic during the last thirty or forty years is reviewed, and a consideration of the diverse ways in which these key points can be generalized allows us to survey some issues in the development of the field in the last twenty to thirty years.

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Categorical Abstract Algebraic Logic: Compatibility Operators and Correspondence Theorems

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An analysis of closure spaces associated with those sentential logics which admit various deduction theorems and it is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.

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Congruence quasi-orderability in subtractive varieties

  • P. Aglianò
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2001
Abstract In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderable. Though this concept has its origin in abstract algebraic logic, it seems to be worth

Fregean subtractive varieties with definable congruence

  • P. Aglianò
  • Mathematics
    Journal of the Australian Mathematical Society
  • 2001
Abstract In this paper we investigate subtractive varieties of algebras that are Fregean in order to get structure theorems about them. For instance it turns out that a subtractive variety is Fregean