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
We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the ...We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.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.
文摘We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is given and, under the calmness property of a set, the right continuity of the size function with respect to both arguments is established. Finally, a classification of its points of discontinuity is given.
