论文信息 - On Positive Relational Calculi

On Positive Relational Calculi

We discuss the question of inclusions between positive relational terms and some of its aspects, using the form of a dialogue. Two possible approaches to the problem are emphasized: natural deduction and graph manipulations. Both provide sound and complete calculi for proving the valid inclusions, supporting nice strategies to obtain proofs in normal form, but the latter appears to present several advantages, which are discussed.

[1] Roger D. Maddux,et al. Relation-Algebraic Semantics , 1996, Theor. Comput. Sci..

[2] Paulo A. S. Veloso,et al. Reasoning with Graphs , 2006, WoLLIC.

[3] W. W. Wadge,et al. A Complete Natural Deduction System for the Relational Calculus , 1975 .

[4] D. Prawitz. Natural Deduction: A Proof-Theoretical Study , 1965 .

[5] Dirk van Dalen,et al. Logic and structure , 1980 .

[6] Alfred Tarski,et al. Relational selves as self-affirmational resources , 2008 .

[7] Hajnal Andréka,et al. Representations of distributive lattice-ordered semigroups with binary relations , 1991 .

[8] Roger D. Maddux,et al. A sequent calculus for relation algebras , 1983, Ann. Pure Appl. Log..

[9] Boris M. Schein,et al. Relation algebras and function semigroups , 1970 .

[10] R. Lyndon. THE REPRESENTATION OF RELATIONAL ALGEBRAS , 1950 .

[11] J. Donald Monk,et al. Nonfinitizability of Classes of Representable Cylindric Algebras , 1969, J. Symb. Log..

[12] R. Lyndon. THE REPRESENTATION OF RELATION ALGEBRAS, II , 1956 .

[13] P. Veloso,et al. Fork Algebras: Past, Present and Future , 2004 .