{"title":"Semantics of normal logic programs and contested information","authors":"Shekhar Pradhan","doi":"10.1109/LICS.1996.561457","DOIUrl":"https://doi.org/10.1109/LICS.1996.561457","url":null,"abstract":"We propose C4, a four-valued semantics for normal, logic programs. Using this semantics, we define two types of entailment: strong and weak. We show that a normal, logic program strongly entails a sentence under C4 if, and only if, the program entails that sentence under the well founded semantics and it weakly entails a sentence if, and only if, the program entails that sentence under the two-valued stable model semantics in case the program has any stable models. We argue that this shows that the difference between the well founded semantics and the stable model semantics can be characterized in terms of their attitude to what we call contested information. We use this insight to propose a general theory of contested reasoning.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"53 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132287079","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":"Counting module quantifiers on finite linearly ordered trees","authors":"Juha Nurmonen","doi":"10.1109/LICS.1996.561465","DOIUrl":"https://doi.org/10.1109/LICS.1996.561465","url":null,"abstract":"We give a combinatorial method for proving elementary equivalence in first-order logic FO with counting module n quantifiers D/sub n/. Inexpressibility results for FO(D/sub n/) with built-in linear order are also considered. We show that certain divisibility properties of word models are not definable in FO(D/sub n/). We also show that the height of complete n-ary trees cannot be expressed in FO(D/sub n/) with linear order. Interpreting the predicate y=nx as a complete n-ary tree, we show that the predicate y=(n+1)x cannot be defined in FO(D/sub n/) with linear order. This proves the conjecture of Niwinski and Stolboushkin (1993). We also discuss connection between our results and the well-known open problem in circuit complexity theory, whether ACC=NC/sup 1/.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115699199","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":"Completing partial combinatory algebras with unique head-normal forms","authors":"I. Bethke, J. Klop, R. D. Vrijer","doi":"10.1109/LICS.1996.561461","DOIUrl":"https://doi.org/10.1109/LICS.1996.561461","url":null,"abstract":"In this note, we prove that having unique head-normal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CL-terms as well as the pca of natural numbers with partial recursive function application can be extended to total combinatory algebras.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117256033","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":"Solving linear equations over polynomial semirings","authors":"P. Narendran","doi":"10.1109/LICS.1996.561463","DOIUrl":"https://doi.org/10.1109/LICS.1996.561463","url":null,"abstract":"We consider the problem of solving linear equations over various semirings. In particular, solving of linear equations over polynomial rings with the additional restriction that the solutions must have only non-negative coefficients is shown to be undecidable. Applications to undecidability proofs of several unification problems are illustrated, one of which, unification modulo one associative-commutative function and one endomorphism, has been a long-standing open problem. The problem of solving multiset constraints is also shown to be undecidable.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131016205","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":"Game semantics and abstract machines","authors":"V. Danos, Hugo Herbelin, L. Regnier","doi":"10.1109/LICS.1996.561456","DOIUrl":"https://doi.org/10.1109/LICS.1996.561456","url":null,"abstract":"The interaction processes at work by M. Hyland and L. Ong (1994) (HO) and S. Abramsky et al. (1994) (AJM) new game semantics are two preexisting paradigmatic implementations of linear head reduction: respectively Krivine's abstract machine and Girard's interaction abstract machine. There is a simple and natural embedding of AJM-games to HO-games, mapping strategies to strategies and reducing AJM definability (or full abstraction) property to HO's one.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127900437","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":"Relating word and tree automata","authors":"O. Kupferman, S. Safra, Moshe Y. Vardi","doi":"10.1109/LICS.1996.561360","DOIUrl":"https://doi.org/10.1109/LICS.1996.561360","url":null,"abstract":"In the automata-theoretic approach to verification, we translate specifications to automata. Complexity considerations motivate the distinction between different types of automata. Already in the 60's, it was known that deterministic Buchi word automata are less expressive than nondeterministic Buchi word automata. The proof is easy and can be stated in a few lines. In the late 60's, Rabin proved that Buchi tree automata are less expressive than Rabin tree automata. This proof is much harder. In this work we relate the expressiveness gap between deterministic and nondeterministic Buchi word automata and the expressiveness gap between Buchi and Rabin tree automata. We consider tree automata that recognize derived languages. For a word language L, the derived language of L, denoted L/spl Delta/, is the set of all trees all of whose paths are in L. Since often we want to specify that all the computations of the program satisfy some property, the interest in derived languages is clear. Our main result shows that L is recognizable by a nondeterministic Buchi word automaton but not by a deterministic Buchi word automaton iff L/spl Delta/ is recognizable by a Rabin tree automaton and not by a Buchi tree automaton. Our result provides a simple explanation to the expressiveness gap between Buchi and Rabin tree automata. Since the gap between deterministic and nondeterministic Buchi word automata is well understood, our result also provides a characterization of derived languages that can be recognized by Buchi tree automata. Finally, it also provides an exponential determinization of Buchi tree automata that recognize derived languages.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128939329","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":"Linear logic, monads and the lambda calculus","authors":"Nick Benton, P. Wadler","doi":"10.1109/LICS.1996.561458","DOIUrl":"https://doi.org/10.1109/LICS.1996.561458","url":null,"abstract":"Models of intuitionistic linear logic also provide models of Moggi's computational metalanguage. We use the adjoint presentation of these models and the associated adjoint calculus to show that three translations, due mainly to Moggi, of the lambda calculus into the computational metalanguage (direct, call-by-name and call-by-value) correspond exactly to three translations, due mainly to Girard, of intuitionistic logic into intuitionistic linear logic. We also consider extending these results to languages with recursion.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134452052","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":"An Until hierarchy for temporal logic","authors":"K. Etessami, T. Wilke","doi":"10.1109/LICS.1996.561310","DOIUrl":"https://doi.org/10.1109/LICS.1996.561310","url":null,"abstract":"We prove there is a strict hierarchy of expressive power according to the Until depth of linear temporal logic (TL) formulas: for each k, there is a very natural property that is not expressible with k nestings of Until operators, regardless of the number of applications of other operators, but is expressible by a formula with Until depth k+1. Our proof uses a new Ehrenfeucht-Fraisse (EF) game designed specifically for TL. These properties can all be expressed in first-order logic with quantifier depth and size O(log k), and we use them to observe some interesting relationships between TL and first-order expressibility. We then use the EF game in a novel way to effectively characterize (1) the TL properties expressible without Until, as well as (2) those expressible without both Until and Next. By playing the game \"on finite automata\", we prove that the automata recognizing languages expressible in each of the two fragments have distinctive structural properties. The characterization for the first fragment was originally proved by Cohen, Perrin, and Pin (1993) using sophisticated semigroup-theoretic techniques. They asked whether such a characterization exists for the second fragment. The technique we develop is general and can potentially be applied in other contexts.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120944741","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 structure of queries in constraint query languages","authors":"Michael Benedikt, L. Libkin","doi":"10.1109/LICS.1996.561300","DOIUrl":"https://doi.org/10.1109/LICS.1996.561300","url":null,"abstract":"We study the structure of first-order and second-order queries over constraint databases. Constraint databases are formally modeled as finite relational structures embedded in some fixed infinite structure. We concentrate on problems of elimination of constraints, reducing quantification range to the active domain of the database and obtaining new complexity bounds. We show that for a large class of signatures, including real arithmetic constraints, unbounded quantification can be eliminated. That is, one can transform a sentence containing unrestricted quantification over the infinite universe to get an equivalent sentence in which quantifiers range over the finite relational structure. We use this result to get a new complexity upper bound on the evaluation of real arithmetic constraints. We also expand upon techniques for getting upper bounds on the expressiveness of constraint query languages, and apply it to a number of first-order and second-order query languages.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130821901","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":"Decidability problems for the prenex fragment of intuitionistic logic","authors":"A. Degtyarev, A. Voronkov","doi":"10.1109/LICS.1996.561467","DOIUrl":"https://doi.org/10.1109/LICS.1996.561467","url":null,"abstract":"We develop a constraint-based technique which allows one to prove decidability and complexity results for sequent calculi. Specifically, we study decidability problems for the prenex fragment of intuitionistic logic. We introduce an analogue of Skolemization for intuitionistic logic with equality, prove PSPACE-completeness of two fragments of intuitionistic logic with and without equality and some other results. In the proofs, we use a combination of techniques of constraint satisfaction, loop-free sequent systems of intuitionistic logic and properties of simultaneous rigid E-unification.","PeriodicalId":382663,"journal":{"name":"Proceedings 11th Annual IEEE Symposium on Logic in Computer Science","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127209011","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}