%0 Journal Article %1 Ginsberg88 %A Ginsberg, Matthew L. %D 1988 %J Computational Intelligence %K ai logic %P 265--316 %T Multivalued logics: A uniform approach to reasoning in artificial intelligence %U http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.4091 %V 4 %X This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including first-order theorem provers, assumption-based truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscription can be subsumed under a single general framework. We begin by defining this framework, which is based on a mathematical structure known as a bilattice. We present a formal definition of inference using this structure, and show that this definition generalizes work involving atms's and some simple nonmonotonic logics. Following the theoretical description, we describe a constructive approach to inference in this setting; the resulting generalization of both conventional inference and atms's is achieved without incurring any substantial computational overhead. We show that our approach can also be used to implement a default reasoner, and discuss a combination of default and atms methods that enables us to formally describe an "incremental " default reasoning system. This incremental system does not need to perform consistency checks before drawing tentative conclusions, but can instead adjust its beliefs when a default premise or conclusion is overturned in the face of convincing contradictory evidence. The system is therefore much

@article{Ginsberg88, abstract = {This paper describes a uniform formalization of much of the current work in AI on inference systems. We show that many of these systems, including first-order theorem provers, assumption-based truth maintenance systems (atms's) and unimplemented formal systems such as default logic or circumscription can be subsumed under a single general framework. We begin by defining this framework, which is based on a mathematical structure known as a bilattice. We present a formal definition of inference using this structure, and show that this definition generalizes work involving atms's and some simple nonmonotonic logics. Following the theoretical description, we describe a constructive approach to inference in this setting; the resulting generalization of both conventional inference and atms's is achieved without incurring any substantial computational overhead. We show that our approach can also be used to implement a default reasoner, and discuss a combination of default and atms methods that enables us to formally describe an "incremental " default reasoning system. This incremental system does not need to perform consistency checks before drawing tentative conclusions, but can instead adjust its beliefs when a default premise or conclusion is overturned in the face of convincing contradictory evidence. The system is therefore much}, added-at = {2009-02-04T18:01:59.000+0100}, author = {Ginsberg, Matthew L.}, biburl = {https://www.bibsonomy.org/bibtex/2985e009b556d6c14a6147014b95efb51/neilernst}, interhash = {3102719b685522abd7341d8fba0795ea}, intrahash = {985e009b556d6c14a6147014b95efb51}, journal = {Computational Intelligence}, keywords = {ai logic}, pages = {265--316}, timestamp = {2009-02-04T18:01:59.000+0100}, title = {Multivalued logics: A uniform approach to reasoning in artificial intelligence}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.4091}, volume = 4, year = 1988 }