Titlebook: Aristotelian Assertoric Syllogistic; Incorporating the Ar Mohamed A. Amer Book 2021 The Author(s), under exclusive license to Springer Natu

Locale

Variations on ,(,),Two variations on .(.) are provided. The interrelationships among .(.) and these two variations are discussed.

Aspiration

Direct Completion of Direct Deduction,Direct deduction is augmented by five more rules so that it becomes equivalent to general deduction from any consistent set of categorical sentences.

憎恶

Models of ,(,) Revisited,General .(.)-models are fully characterized. Moreover, defining the notions of core structures and core models, as well as other syntactical and semantical notions, a deeper discussion of .(.)-models is made possible and direct ways to assign order models and partial order models to consistent sets of categorical sentences are provided.

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外星人

残忍

Independence,Regarding the natural deduction formalization of AAS, the notions of independence and weak independence are defined and discussed for different deduction systems.

胡言乱语

藐视

Algebraic Interpretation of ,(,),It is shown how .(.) may be interpreted in expansions of partial algebras satisfying some conditions. Interrelationships among these expansions, order models, and partial order models are discussed.

植物群

Annihilators: Embedding the Partial into a Total,Introducing the notions of annihilators and annihilator algebras, it is shown how a partial algebra may be embedded in a total annihilator algebra. Interrelationships among these algebras, their reducts, subreducts, and the order structures induced by them are discussed.

Munificent

Back to Algebraic Interpretation,Interpretation of .(.) in expansions of annihilator algebras satisfying some conditions, is defined. The interrelationships among these expansions, the expansions introduced in Chap. ., and Venn models are discussed.