Tractable subsets of first-order logic are a central topic in AI research. Several these formalisms have been used as the basis for probabilistic languages. However, intractable, losing original motivation. Here we propose first non-trivially tractable language. It is subset Markov logic, and uses class part hierarchies to control complexity. We call it TML (Tractable Logic). show that knowledg...

suhrawardi’s logic of the hikmat al-ishraq is basically modal. so to understand his modal logic one first has to know the non-modal part upon which his modal logic is built. in my previous paper ‘suhrawardi on syllogisms’(3) i discussed the former in detail. the present paper is an exposition of his treatment of modal syllogisms. on the basis of some reasonable existential presuppositions and a...

Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets...

The notion of $f$-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of $f$-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.

Logic should have been defined as the unity of contradiction between logic director and logic implementation. Chinese Daoism asserts that everything is defined in the unity of opposites, namely yin and yang, accordingly yang conducts change and yin brings it up (I-Ching, also known as Book of Changes). In this way logic is redefined in an indeterminate style to facilitate “both A and Anti-A” et...