In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neit...In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neither of the ideas holds,which makes it difficult to give a natural semantics for connexive logic.By combining Kleene's three valued logic and Lewis'conditional logic,we propose a new natural semantics for connexive logic.We give four ax-iomatic systems characterizing different classes of selection models in the new semantics.We prove soundness and completeness of these logics and compare them with some comexive 1og-ics in the literature.展开更多
基金supported by the MOE Project of Humanities and Social Sciences of China(Grant No.21YJA72040001)。
文摘In connexive logic,two fundamental ideas are observed:first,no proposition im-plies or is implied by its own negation;second,if a proposition implies p then it will not imply the negation of 4p.In classical logic,neither of the ideas holds,which makes it difficult to give a natural semantics for connexive logic.By combining Kleene's three valued logic and Lewis'conditional logic,we propose a new natural semantics for connexive logic.We give four ax-iomatic systems characterizing different classes of selection models in the new semantics.We prove soundness and completeness of these logics and compare them with some comexive 1og-ics in the literature.
