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A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation

100%

Kürbis N.

Bulletin of the Section of Logic

2019

tom 48

nr 2

81-97

This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ℩x[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts

75%

Braüner T.

Bulletin of the Section of Logic

2022

tom 51

nr 2

143-162

This paper is about non-labelled proof-systems for hybrid logic, that is, proofsystems where arbitrary formulas can occur, not just satisfaction statements. We give an overview of such proof-systems, focusing on analytic systems: Natural deduction systems, Gentzen sequent systems and tableau systems. We point out major results and we discuss a couple of striking facts, in particular that nonlabelled hybrid-logical natural deduction systems are analytic, but this is not proved in the usual way via step-by-step normalization of derivations.

Ograniczanie wyników

2 Bulletin of the Section of Logic

1 Braüner T.

1 Kürbis N.

1 2022

1 2019

Wyniki wyszukiwania

A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation

Analytic Non-Labelled Proof-Systems for Hybrid Logic: Overview and a couple of striking facts