[AB75]

Alan Ross Anderson and Nuel D. Belnap, Jr., *Entailment: The Logic of Relevance and Necessity*, volume I, Princeton University Press, 1975.

[ABD92]

Alan Ross Anderson, Nuel D. Belnap Jr., and J. Michael Dunn, *Entailment: The Logic of Relevance and Necessity*, volume II, Princeton University Press, 1992.

[AD93]

Gerard Allwein and J. Michael Dunn, 'Kripke models for linear logic', *Journal of Symbolic Logic* 58: 514-545, 1993.

[All92]

Gerard Allwein, *The Duality of Algebraic and Kripke Models for Linear Logic*, PhD thesis, Indiana University, 1992.

[AM98]

Gerard Allwein and Wendy MacCaull, 'Duality for complete lattices', Technical report, Indiana University, 1998.

[BG93]

Carolyn Brown and Douglas Gurr, 'A representation theorem for quantales', *Journal of Pure and Applied Algebra* 85: 27-42, 1993.

[Che80]

Brian F. Chellas, *Modal Logic, an Introduction*, Cambridge University Press, 1980.

[Dun70]

J. Michael Dunn, 'Algebraic completeness results for r-mingle and its extensions', *Journal of Symbolic Logic* 35:1-13, 1970.

[Dun90]

J. Michael Dunn, 'Gaggle theory: An abstraction of galois connections and residuation with applications to negation and various logical operations', in *Logics in AI, Proceedings European Workshop JELIA, LNCS 478*, Springer-Verlag, 1990.

[Dun93]

J. Michael Dunn, 'Partial gaggle theory applied to logics with restricted structural rules', in K. Došen and P. Schroeder-Heister, editors, *Substructural Logics*, 1993.

[Gab96]

Dov Gabbay, 'Fibered semantics and the weaving of logics. Part 1: Modal and intuitionistic logics', *Journal of Symbolic Logic* 61:1055-1119, 1996.

[HJ87]

C.A.R. Hoare and He Jifeng, 'A weakest pre-specification', *Inform. Process. Lett.* 24: 127-132, 1987.

[Mac97]

Wendy MacCaull, 'Relational proof theory for linear and other substructural logics', *Journal of the Interest Group of Pure and Applied Logic* 5:673-697, 1997.

[Mac98]

Wendy MacCaull, 'Relational semantics and a relational proof system for full Lambek calculus', *Journal of Symbolic Logic* 63:623-637, 1998.

[MN95]

C. J. Mulvey and M. Nawaz, 'Quantales: Quantal sets', in Ulrich Hoehle and Erich Peter Klement, editors, *Non-Classical Logics and Their Applications to Fuzzy Subsets*, Kluwer Academic Publishers, 1995.

[MP92]

Chris Mulvey and Joan Wick Pelletier, 'The quantization of the calculus of relations', in “*Canadian Mathematical Society Conference Proceedings*”*, American Mathematical Society, Providence*, volume 13, pages 345-360, 1992.

[MP00]

Chris Mulvey and Joan Wick Pelletier, 'The quantization of points', to appear in Journal of Pure and Applied Algebra, 2000.

[Mul86]

Chris Mulvey, &, *Suppl. Rend. Circ. Mat. Palermo Ser. II* 12:99-104, 1986.

[OK85]

Hiroakira Ono and Yuichi Komuri, 'Logics without the contraction rule', *Journal of Symbolic Logic* 50:169-201, 1985.

[Ono93]

Hiroakira Ono, 'Semantics for substructural logics', in K. Došen and P. Schroeder-Heister, editors, *Substructural Logics*, pages 259-291, 1993.

[OrVł92]

Ewa Or9łowska, 'Relational proof system for relevant logics', *Journal of Symbolic Logic* 57:1425-1440, 1992.

[OrVł94]

Ewa Or9łowska, 'Relational semantics for logics: formulas are relations', in Jan Wolenski, editor, *Philosophical Logic in Poland*, pages 167-186, Kluwer, 1994.

[OrVł96]

Ewa Or9łowska, 'Relational environment for semigroup logics', in André Fuhrmann and Hans Rott, editors, *Logic, Action, and Information, Essays on Logic in Philosophy and Artificial Intelligence*, pages 351-391, Walter de Gruyter, (Berlin, New York), 1996.

[PR97]

J. Wick Pelletier and J. RosickÝ, 'Simple involutive quantales', *Journal of Algebra* 195:367-386, 1997.

[Pri72]

H. A. Priestley, 'Ordered topological spaces and the representation of distributive lattices', in *Proceedings of the London Mathematical Society*, volume 24, pages 507-530, 1972.

[RM73]

Richard Routley and Robert K. Meyer, 'The semantics of entailment', in H. Leblanc, editor, *Truth, Syntax, and Modality*, pages 194-243, North Holland, 1973.

[Ros90]

Kimmo Rosenthal, *Quantales and their applications*, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, Copublished in the United States with John Wiley and Sons, Inc., New York, 1990.

[RS63]

Helena Rasiowa and Roman Sikorski, *The Mathematics of Metamathematics*, Polish Scientific Publishers, 1963.

[Sto36]

M.H. Stone, 'The theory of representation for Boolean algebras', *Transactions of the American Mathematical Society* 40:37-111, 1936.

[Urq78]

Alasdair Urquhart, 'A topological representation theory for lattices', *Algebra Universalis* 8:45-58, 1978.

[vB84]

Johan van Benthem, 'Correspondence theory', in *Handbook of Philosophical Logic, Vol. II, Synthese Lib. 165*, pages 167-247, D. Reidel Publishing Company, 1984.