{"product_id":"multiple-conclusion-logic-paperback-9780521093323","title":"Multiple-Conclusion Logic (Paperback \/ softback) 9780521093323","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMultiple-Conclusion Logic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis is a sustained study of the subject and is certain to stimulate further research.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eD. J. Shoesmith (Author), T. J. Smiley (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521093323, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 11 January 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e416 pages\u003cbr\u003e22.9 x 15.2 x 2.3 cm, 0.6 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eMultiple-conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks the fundamental ideas of logic to take account of multiple conclusions, and investigates the connections between multiple - and single - conclusion calculi. Part II draws on graph theory to discuss the form and validity of arguments independently of particular logical systems. Part III contrasts the multiple - and the single - conclusion treatment of one and the same subject, using many-valued logic as the example; and Part IV shows how the methods of 'natural deduction' can be matched by direct proofs using multiple conclusions.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Introduction\u003cbr\u003e Part I. Multiple and Single Conclusions\u003cbr\u003e 1. Single-conclusion calculi\u003cbr\u003e 2. Multiple-conclusion calculi\u003cbr\u003e 3. Tree proofs\u003cbr\u003e 4. Axiomatisability\u003cbr\u003e 5. Counterparts\u003cbr\u003e 6. Infinite rules\u003cbr\u003e Part II. Graph Proofs\u003cbr\u003e 7. Graph arguments\u003cbr\u003e 8. Kneale proofs\u003cbr\u003e 9. Cross-reference\u003cbr\u003e 10. Abstract proofs\u003cbr\u003e 11. Single-conclusions proofs\u003cbr\u003e 12. Infinite proofs\u003cbr\u003e Part III: Many-valued Logic\u003cbr\u003e 13. Many-valued calculi\u003cbr\u003e 14. matrices\u003cbr\u003e 15. Many-valuedness\u003cbr\u003e 16. Counterparts\u003cbr\u003e 17. Categoricity\u003cbr\u003e 18. Two-valued logic\u003cbr\u003e 19. Axiomatisation\u003cbr\u003e Part IV. Natural Deduction\u003cbr\u003e 20. Natural Deduction\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006382985496,"sku":"9780521093323","price":41.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521093323i_056cbb3b-ce75-43b8-b73e-debb1cbedd2d.jpg?v=1694970506","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/multiple-conclusion-logic-paperback-9780521093323","provider":"Freshly Printed Books","version":"1.0","type":"link"}