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The finite model property for knotted extensions of propositional linear logic

  • C. J. van Alten (a1)

The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: . It is proved that the class of algebraic models for such a logic has the finite embeddability property, meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property with respect to its algebraic semantics and hence that the logic is decidable.

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[1] W. J. Blok and C. J. van Alten , The finite embeddability property for residuated lattices, pocrims and BCK-algebras, Algebra Universalis, vol. 48 (2002), no. 3, pp. 253271.

[3] R. Hori , H. Ono , and H. Schellinx , Extending intuitionistic logic with knotted structural rules, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 219242.

[5] P. Lincoln , J. Mitchell , A. Scedrov , and N. Shankar , Decision problems for propositional linear logic, Annals of Pure and Applied Logic, vol. 56 (1992), pp. 239311.

[10] C. J. van Alten and J. G. Raftery , Rule separation and embedding theorems for logics without weakening, Stadia Logica, vol. 76 (2004), pp. 241274.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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