Monadic pseudo-equality algebras
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In this paper, we introduce the concept of monadic pseudo-equality algebras and obtain some related properties. We study the relations between monadic pseudo-equality algebras, monadic bounded hoops and monadic pseudo-BCI-algebras. Then, we introduce and study monadic deductive systems and monadic congruences and discuss the relations between them. We use monadic deductive systems to define uniform topology on pseudo-equality algebras and obtain some topological results. Finally, the corresponding logic (monadic invariant pseudo-equality logic) is constructed and the soundness and completeness of this logic are proved based on monadic invariant pseudo-equality algebras.
KeywordsMonadic pseudo-equality algebra Monadic deductive system Uniform structure Monadic invariant pseudo-equality logic
The author would like to express her thanks to referees for their comments and suggestions which improved the paper.
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