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.

An important allegory throughout the history of philosophy is Plato’s allegory of the cave. There are remarkable similarities between this allegory and an allegory from Islamic philosophy—that of western exile (al-ghurba al-gharbiyya) proposed by Suhrawardī. This paper seeks to consider fundamental components and issues within the two allegories, including the issue of the soul as the ...

Introduction Preamble -Aesthetics | Poetry and Islam | Poetry and warlords | Poetry and Afghanistan -Poetry and Kazakhstan | Poetry and the Caucasus | Poetry and the Middle East -Poetic leadership | Poetic protest | Prosaic dialogue Indicative possibilities of reframing strategic engagement Clarification of Islamic views Improvisation in poetic debate -Poetic discourse as a lost art | Poetic en...

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.