Infinite-Valued First-Order Łukasiewicz Logic: Hypersequent Calculi Without Structural Rules and Proof Search for Sentences in the Prenex Form
The rational first-order Pavelka logic is an expansion of the infinite-valued first-order Łukasiewicz logic Ł∀ by truth constants. For this logic, we introduce a cumulative hypersequent calculus G 1 Ł∀ and a noncumulative hypersequent calculus G 2 Ł∀ without structural inference rules. We compare th...
Gespeichert in:
Veröffentlicht in: | Siberian advances in mathematics 2018-04, Vol.28 (2), p.79-100 |
---|---|
1. Verfasser: | |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | The rational first-order Pavelka logic is an expansion of the infinite-valued first-order Łukasiewicz logic Ł∀ by truth constants. For this logic, we introduce a cumulative hypersequent calculus G
1
Ł∀ and a noncumulative hypersequent calculus G
2
Ł∀ without structural inference rules. We compare these calculi with the Baaz–Metcalfe hypersequent calculus GŁ∀ with structural rules. In particular, we show that every GŁ∀-provable sentence is G
1
Ł∀-provable and a Ł∀-sentence in the prenex form is GŁ∀-provable if and only if it is G
2
Ł∀-provable. For a tableau version of the calculus G
2
Ł∀, we describe a family of proof search algorithms that allow us to construct a proof of each G
2
Ł∀-provable sentence in the prenex form. |
---|---|
ISSN: | 1055-1344 1934-8126 |
DOI: | 10.3103/S1055134418020013 |