The Basic Algebra of Game Equivalences
Valentin Gorankov

Abstract:
We give a complete axiomatization of the identities of the basic game
algebra, valid with respect to the abstract game board semantics. We
also show that the additional conditions of termination and
determinacy of game boards do not introduce new valid identities.

En route we introduce a simple translation of game terms into plain
modal logic and thus translate, while preserving validity both ways,
game identities into modal formulae.

The completeness proof is based on reduction of game terms to a
certain `minimal canonical form', using only the axiomatic identities,
and on showing that the equivalence of two minimal canonical terms can
be established from these identities.  

Keyword(s): game algebra, game boards, game equivalence, axiomatization, 
completeness