A comparison between lambek syntactic calculus and intuitionistic linear propositional logic
✍ Scribed by V. Michele Abrusci
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 252 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
A COMPARISON BETWEEN LAMBEK SYNTACTIC CALCULUS ASD INTUITIONISTIC LINEAR PROPOSITIONAL LOGIC by V. MICHELE ABRUSCI in Bari (Italy)
1. Synt,ax
Let us consider LAMBEK'S syntactic calculus LSC as formulated in BUSZKOWSKI [ Z ] in an axiomatization very close to GEmZEN's sequential formalism.
We define the following modification of the language 8 ( I L O ) , called Z ( L I L ) , where ILO is the sequent calculus for intuitionistic linear propositional logic introduced in GIRARD-LAFOKT [4j and investigated in ABRUSCI [l]: delete all the constants, the additive connectives & and 0 , and the exponential connectives ? and !:
add a new multiplicative connective O-; instead of "finite niultisets of formulas " consider "finite sequences of formulas ".