## Journal of Symbolic Logic

### The Finite Model Property for Various Fragments of Intuitionistic Linear Logic

#### Abstract

Recently Lafont [6] showed the finite model property for the multiplicative additive fragment of linear logic (MALL) and for affine logic (LLW), i.e., linear logic with weakening. In this paper, we shall prove the finite model property for intuitionistic versions of those, i.e. intuitionistic MALL (which we call IMALL), and intuitionistic LLW (which we call ILLW). In addition, we shall show the finite model property for contractive linear logic (LLC), i.e., linear logic with contraction, and for its intuitionistic version (ILLC). The finite model property for related substructural logics also follow by our method. In particular, we shall show that the property holds for all of FL and GL$^-$-systems except FL$_c$ and GL$^-_c$ of Ono [11], that will settle the open problems stated in Ono [12].

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 2 (1999), 790-802.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745810

Mathematical Reviews number (MathSciNet)
MR1777787

Zentralblatt MATH identifier
0930.03021

JSTOR

#### Citation

Okada, Mitsuhiro; Terui, Kazushige. The Finite Model Property for Various Fragments of Intuitionistic Linear Logic. J. Symbolic Logic 64 (1999), no. 2, 790--802. https://projecteuclid.org/euclid.jsl/1183745810