Unification on Subvarieties of Pseudocomplemented Distributive Lattices

In this paper subvarieties of pseudocomplemented distributive lattices are classified by their unification type. We determine the unification type of every particular unification problem in each subvariety of pseudocomplemented distributive lattices.

[1]  Petr Cintula,et al.  Admissible rules in the implication-negation fragment of intuitionistic logic , 2010, Ann. Pure Appl. Log..

[2]  V. Gorbunov,et al.  Algebraic theory of quasivarieties , 1998 .

[3]  H. Priestley.  THE CONSTRUCTION OF SPACES DUAL TO PSEUDOCOMPLEMENTED DISTRIBUTIVE LATTICES , 1975 .

[4]  Hilary A. Priestley,et al.  Representation of Distributive Lattices by means of ordered Stone Spaces , 1970 .

[5]  W OJC,et al.  SPLITTINGS OF LATTICES OF THEORIES AND UNIFICATION TYPES , 1601 .

[6]  Tobias Nipkow,et al.  Boolean Unification - The Story So Far , 1989, J. Symb. Comput..

[7]  Claude Kirchner,et al.  Solving Equations in Abstract Algebras: A Rule-Based Survey of Unification , 1991, Computational Logic - Essays in Honor of Alan Robinson.

[8]  Projective distributive p-algebras , 1981, Bulletin of the Australian Mathematical Society.

[9]  Andrzej Wronski.  Transparent Unification Problem , 1995, Reports Math. Log..

[10]  Christopher Butler,et al.  Unification , 1937, Journal of the Irish Medical Association.

[11]  Franz Baader,et al.  Unification theory , 1986, Decis. Support Syst..

[12]  Simone Bova,et al.  Unification and Projectivity in De Morgan and Kleene Algebras , 2014, Order.

[13]  Franz Baader,et al.  Characterization of Unification Type Zero , 1989, RTA.

[14]  Silvio Ghilardi,et al.  Unification in intuitionistic logic , 1999, Journal of Symbolic Logic.

[15]  K. B. Lee,et al.  Equational Classes of Distributive Pseudo-Complemented Lattices , 1970, Canadian Journal of Mathematics.

[16]  Tadeusz Prucnal.  On the structural completeness of some pure implicational propositional calculi , 1972 .

[17]  Silvio Ghilardi,et al.  Unification Through Projectivity , 1997, J. Log. Comput..