Freyd and Scedrov showed that the equational theory of representable allegories (essentially those allegories which have a settheoretic representation as relations) is decidable. This paper proves that the pure equational theory of allegories is decidable.

Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us t...

It is know in topos theory that axiom of choice implies that the topos is Boolean. In this paper we want to prove and generalize this result in the context of allegories. In particular, we will show that partial identities do have complements in distributive allegories with relational sums and total splittings assuming the axiom of choice. Furthermore, we will discuss possible modifications of ...

This article uses psychological and neural theories to illuminate the use of analogies in literary allegories. It shows how new theories of neural representation, encompassing both cognitive and emotional aspects, have the potential to make sense of many kinds of literary comparisons including allegories. The main text analyzed is George Orwell’s Animal Farm, whose effectiveness is discussed us...

In this paper we a language and first-order calculus for formal reasoning about relations based on the theory of allegories. Since allegories are categories the language is typed in Church-style. We show soundness and completeness of the calculus and demonstrate its usability by presenting the RelAPS system; a proof assistant for relational categories based on the calculus presented here.

Groups are one of the most fundamental notions in mathematics. This paper provides a foundation of group theory in allegories. Almost all results in the paper can be applied to theory of fuzzy groups.

understanding allegories, helps us to give a clear and accepted interpretation of complex and complicated thoughts, and this is said to be a cultural need. the purpose of this research is to find and recognize the allegories used by meibodi in his mystic interpretation of kashf-ol-asraar. the results of the study show that different kinds of allegories are used in this interpretation; and this ...

In allegories polysemy relates not only to the context and the audience’s understanding but also to the structural characters of these texts. This paper investigates the function of structural and narrative properties in the creation of multiple interpretations of an allegory. Focusing on the events and following a unique story-line is the most important trait in helping to read the alleg...