This paper present* an incremental and Lasy daemon procedure for the fint-order equality theory over a Herforand universe (Clark equality theory) as well as for that of rational trees. The pruceduie is based on a conjunctive normal form and consists of two algorithms, one algorithm to decide satisfiability and one for transforming a universally quantified negated constraint into a new constraint in normal form. We will also show that a general formula in either theory can be rewritten into an equivalent normal form, thus providing a general decision procedure. The normal form and the design of the decision procedure have been chosen to meet the requirements of a concurrent constraint Tig language.
{"title":"Finite and Rational Tree Constraints","authors":"Torbjörn Keisu","doi":"10.1093/jigpal/2.2.167","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.167","url":null,"abstract":"This paper present* an incremental and Lasy daemon procedure for the fint-order equality theory over a Herforand universe (Clark equality theory) as well as for that of rational trees. The pruceduie is based on a conjunctive normal form and consists of two algorithms, one algorithm to decide satisfiability and one for transforming a universally quantified negated constraint into a new constraint in normal form. We will also show that a general formula in either theory can be rewritten into an equivalent normal form, thus providing a general decision procedure. The normal form and the design of the decision procedure have been chosen to meet the requirements of a concurrent constraint Tig language.","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130095846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many diierent ways. They map out structures that are relevant to a number of diierent applications. S1, S2 and S3 however, are not so lucky. They are little studied, and used even less. It has become clear that the structures described by S4 and S5 are important in diierent ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of diierent uses. We will examine a substructural logic which is important in a number of diierent ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information ow. In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. 1 Relation algebras Relation algebras are an interesting generalisation of Boolean algebras. For our purposes we will only need a fragment of the general relation algebras studied by Tarski and others 27]. Take a class of objects and a collection of binary relations on this class. There are a number of ways to form new relations from old: the Boolean con-nectives are some, but there are also others. Pairs of relations can be composed: a and b are related by the composition of and (written) just when for some c, aac and ccb. Composition is associative, but not commutative or idempotent. The identity relation 1' satisses 1' = = 1'. Any relation has a converse, written , which satisses = and a number of other identities. An abstract positive relation algebra is a 6-tuple hR; ; ; 1; ;1'i, such that hR; ; ; 1i is a distributive lattice with top element 1 (the full relation), (composition) is an associative binary operation on R with identity 1' (the identity relation). In addition, composition distributes over …
{"title":"A Useful Substructural Logic","authors":"Greg Restall","doi":"10.1093/jigpal/2.2.137","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.137","url":null,"abstract":"Formal systems seem to come in two general kinds: useful and useless. This is painting things starkly, but the point is important. Formal structures can either be used in interesting and important ways, or they can languish unused and irrelevant. Lewis' modal logics are good examples. The systems S4 and S5 are useful in many diierent ways. They map out structures that are relevant to a number of diierent applications. S1, S2 and S3 however, are not so lucky. They are little studied, and used even less. It has become clear that the structures described by S4 and S5 are important in diierent ways, while the structures described by S1 to S3 are not so important. In this paper, we will see another formal system with a number of diierent uses. We will examine a substructural logic which is important in a number of diierent ways. The logic of Peirce monoids, inspired by the logic of relations, is useful in the independent areas of linguistic types and information ow. In what follows I will describe the logic of Peirce monoids in its various guises, sketch out its main properties, and indicate why it is important. As proofs of theorems are readily available elsewhere in the literature, I simply sketch the relevant proofs here, and point the interested reader to where complete proofs can be found. 1 Relation algebras Relation algebras are an interesting generalisation of Boolean algebras. For our purposes we will only need a fragment of the general relation algebras studied by Tarski and others 27]. Take a class of objects and a collection of binary relations on this class. There are a number of ways to form new relations from old: the Boolean con-nectives are some, but there are also others. Pairs of relations can be composed: a and b are related by the composition of and (written) just when for some c, aac and ccb. Composition is associative, but not commutative or idempotent. The identity relation 1' satisses 1' = = 1'. Any relation has a converse, written , which satisses = and a number of other identities. An abstract positive relation algebra is a 6-tuple hR; ; ; 1; ;1'i, such that hR; ; ; 1i is a distributive lattice with top element 1 (the full relation), (composition) is an associative binary operation on R with identity 1' (the identity relation). In addition, composition distributes over …","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126284224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Methods for dealing with a Horn logic program and one goal are well-known and successful. Here we are concerned with treating logic programs enhanced by some negative literals using the same methods, in particular SLD-resolution. We describe the approach and show its correctness. The result can be applied to default reasoning and has some relevance for model elimination based theorem proving.
{"title":"Applying SLD-resolution to a class of non-Horn logic programs","authors":"G. Antoniou, E. Langetepe","doi":"10.1093/JIGPAL/2.2.229","DOIUrl":"https://doi.org/10.1093/JIGPAL/2.2.229","url":null,"abstract":"Methods for dealing with a Horn logic program and one goal are well-known and successful. Here we are concerned with treating logic programs enhanced by some negative literals using the same methods, in particular SLD-resolution. We describe the approach and show its correctness. The result can be applied to default reasoning and has some relevance for model elimination based theorem proving.","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126447993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Traditionally logic was considered as having two branches: deductive and inductive. However the development of the subject from Frege (1879) up to about 1970 brought about a divergence between deductive and inductive logic. It is argued in this paper that developments in artiicial intelligence in the last twenty or so years (particularly logic programming and machine learning) have created a new framework for logic in which deductive and inductive logic can, once again, be treated as similar branches of the same discipline.
{"title":"A Rapprochement between Deductive and Inductive Logic","authors":"D. Gillies","doi":"10.1093/jigpal/2.2.149","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.149","url":null,"abstract":"Traditionally logic was considered as having two branches: deductive and inductive. However the development of the subject from Frege (1879) up to about 1970 brought about a divergence between deductive and inductive logic. It is argued in this paper that developments in artiicial intelligence in the last twenty or so years (particularly logic programming and machine learning) have created a new framework for logic in which deductive and inductive logic can, once again, be treated as similar branches of the same discipline.","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123309528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Computational Intractabilityof Analytic Tableau Methods","authors":"Neil V. Murray, Erik Rosenthal","doi":"10.1093/jigpal/2.2.205","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.205","url":null,"abstract":"","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130548207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Review of Deontic Logic in Computer Science: Normative System Specification, John-Jules Ch. Meyer and Roel J. Wieringa (eds.), John Wiley & Sons, Chichester 1993","authors":"S. Hansson","doi":"10.1093/jigpal/2.2.249","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.249","url":null,"abstract":"","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116103005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Review of Nonmonotonic Logic by W. Marek and M. Truszscynski, Springer, 1993","authors":"J. Dix","doi":"10.1093/jigpal/2.2.251","DOIUrl":"https://doi.org/10.1093/jigpal/2.2.251","url":null,"abstract":"","PeriodicalId":267129,"journal":{"name":"Bull. IGPL","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117142373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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