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Safe stratified Datalog with integer order does not have syntax

Alexei P. Stolboushkin, Michael A. Taitslin
1998 ACM Transactions on Database Systems  
Stratified Datalog with integer (gap)-order (or Datalog ¬,<z ) is considered. A Datalog ¬,<z -program is said to be safe iff its bottomup processing terminates on all valid inputs.  ...  We prove that safe Datalog ¬,< z -programs do not have effective syntax in the sense that there is no recursively enumerable set S of safe Datalog ¬,< z -programs such that every safe Datalog ¬,< z -program  ...  While it is known that total Turing machines do not have an effective syntax.  ... 
doi:10.1145/288086.288089 fatcat:auoqlhgptbdqldqchbjklnjnxa

Page 6547 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
The results are then: the set of finite formulas of the domain T does not have an effective syntax; for no decid- able extension T’ of T does there exist a recursive syntax for finite queries; the state-safety  ...  Section 4 deals with stratified Datalog programs over domain Z (with < and =).  ... 

Dedalus: Datalog in Time and Space [chapter]

Peter Alvaro, William R. Marczak, Neil Conway, Joseph M. Hellerstein, David Maier, Russell Sears
2011 Lecture Notes in Computer Science  
These details have a semantics outside Datalog, which increases the complexity of the language or its interpretation, and forces programmers to think operationally.  ...  Given these two features, we address three important properties of programs in a domain-specific manner: a notion of safety appropriate to non-terminating computations, stratified monotonic reasoning with  ...  Observe that the integer value of the timestep does not influence the derivation.  ... 
doi:10.1007/978-3-642-24206-9_16 fatcat:bkbtvsedrrcd5e3ewx6cfwlmvu

Complexity and Expressive Power of Disjunction and Negation in Limit Datalog

Mark Kaminski, Bernardo Cuenca Grau, Egor V. Kostylev, Ian Horrocks
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Limit Datalog is a fragment of Datalogℤ—the extension of Datalog with arithmetic functions over the integers—which has been proposed as a declarative language suitable for capturing data analysis tasks  ...  In limit Datalog programs, all intensional predicates with a numeric argument are limit predicates that keep maximal (or minimal) bounds on numeric values.  ...  Kaminski et al. [2017; 2018] have recently proposed the language of limit Datalog programs-a decidable variant of Datalog equipped with stratified negation and arithmetic Copyright c 2020, Association  ... 
doi:10.1609/aaai.v34i03.5676 fatcat:2r7uhzrdaje23ol4bv7x3lrbd4

Safe stratified datalog with integer order programs [chapter]

Peter Z. Revesz
1995 Lecture Notes in Computer Science  
Termination cannot be guaranteed in Strati ed Datalog with integer (gap)-order, or Datalog :;< Z , programs on generalized databases because they can express any Turingcomputable function 23].  ...  This paper introduces a restriction of Datalog :;< Z that can express only computable queries. The restricted language has a high expressive power and a non-elementary data complexity.  ...  The syntax of Strati ed Datalog with integer (gap)-order programs, denoted strati ed Datalog :;<Z , is that of Datalog <Z except in the rule bodies expressions of the form :p(x 1 ; : : : ; x n ) can also  ... 
doi:10.1007/3-540-60299-2_10 fatcat:lkyvxu2pc5ei3jeq4winvjvu2e

On problems of databases over a fixed infinite universe

Oleg Belegradek, Alexei Stolboushkin, Michael Taitslin
1999 Banach Center Publications  
We prove that safe Datalog ¬,<z -programs do not have any effective syntax.  ...  This class includes all o -minimal domains, but also the ordered group of integer numbers and the ordered semigroup of natural numbers, and some other domains.  ...  The set of finite formulas of the domain T does not have an effective syntax.  ... 
doi:10.4064/-46-1-23-62 fatcat:axt746x7pzbgpirsymwyktt6f4

Stratified Negation in Limit Datalog Programs

Mark Kaminski, Bernardo Cuenca Grau, Egor V. Kostylev, Boris Motik, Ian Horrocks
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
Rules in this language, however, do not allow for negation. In this paper, we study an extension of limit programs with stratified negation-as-failure.  ...  We also identify a fragment with tractable data complexity and sufficient expressivity to capture many relevant tasks.  ...  Preliminaries In this section we recapitulate the syntax and semantics of Datalog programs with integer arithmetic and stratified negation (see e.g., [Dantsin et al., 2001] for an excellent survey).  ... 
doi:10.24963/ijcai.2018/259 dblp:conf/ijcai/KaminskiGKMH18 fatcat:jjfp73v2xnayfakqjyiazrrosu

NP Datalog: a Logic Language for Expressing NP Search and Optimization Problems [article]

Sergio Greco, Cristian Molinaro, Irina Trubitsyna, Ester Zumpano
2009 arXiv   pre-print
Specifically, first a language obtained by extending (positive) Datalog with intuitive and efficient constructs (namely, stratified negation, constraints and exclusive disjunction) is introduced.  ...  This language, called NP Datalog, captures the power of Datalog with unstratified negation in expressing search and optimization problems. A system prototype implementing NP Datalog is presented.  ...  NP-SPEC programs have a structure similar to the one of NP Datalog programs, although from the syntax point of view, the use of meta-predicates, in some cases, does not make programs shorter and more intuitive  ... 
arXiv:0911.2785v1 fatcat:seapr5odo5flxmdmkm5lmd25ly

Seamless deductive inference via macros

Arash Sahebolamri, Thomas Gilray, Kristopher Micinski
2022 Proceedings of the 31st ACM SIGPLAN International Conference on Compiler Construction  
We leverage Rust's trait system to extend Datalog semantics with non-powerset lattices, much like Flix, and with user-defined data types much like Formulog and Souffle.  ...  We present an approach to integrating state-of-art bottom-up logic programming within the Rust ecosystem, demonstrating it with Ascent, an extension of Datalog that performs well against comparable systems  ...  Ascent does not have that requirement, and does not take advantage of these efficient join algorithms currently.  ... 
doi:10.1145/3497776.3517779 fatcat:fkotic4oszeqhan2imae6c6h3e

Translating NP-SPEC into ASP [article]

Mario Alviano, Wolfgang Faber
2013 arXiv   pre-print
Despite the fact that the semantics of the language was given by referring to Datalog with circumscription, which is very close to ASP, so far the only existing implementations are by means of ECLiPSe  ...  DLV currently does not support negative integers and it does not provide constructs corresponding to abs andˆ.  ...  Stratified Datalog Program. The stratified Datalog program is written using < −− as the rule implication symbol. It may contain built-in predicates (==, <, >, >=, <=, !  ... 
arXiv:1301.1385v1 fatcat:j5k67nqyczcuvla44eclolvpoi

Restricted Predicates for Hypothetical Datalog

Fernando Sáenz-Pérez
2015 Electronic Proceedings in Theoretical Computer Science  
While in that work positive assumptions for both facts and rules can occur in the premise, negative assumptions are not allowed.  ...  Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies.  ...  Though there have been some works regarding implementations [25] , as far as we know there has not been an implementation of hypothetical Datalog with intensional deletions.  ... 
doi:10.4204/eptcs.200.5 fatcat:ylgwqaal6rfmfadlhwwymt2bs4

Outer Joins in a Deductive Database System

Fernando Sáenz-Pérez
2012 Electronical Notes in Theoretical Computer Science  
So, as SQL statements are ultimately solved by a Datalog engine, it became a need to integrate null-related operations into Datalog in order to support a wider set of SQL.  ...  Outer joins are extended relational algebra operations intended to deal with unknown information represented with null values.  ...  Nulls are internally represented with the term '$NULL'(IdNumber), where IdNumber is a unique integer which does not occur in any other null.  ... 
doi:10.1016/j.entcs.2011.12.007 fatcat:pkmslg4xq5dwhgbma35rojnzxq

A formal framework for reflective database access control policies

Lars E. Olson, Carl A. Gunter, P. Madhusudan
2008 Proceedings of the 15th ACM conference on Computer and communications security - CCS '08  
We propose the use of Transaction Datalog as a formal framework for expressing reflective access control policies.  ...  However, such policies introduce new interactions between data managed by different users, and can lead to unexpected results if not carefully written and analyzed.  ...  For a database with state S and transaction base P with rules that contain no retractions and are safely rewritable, if a given permission does not exist in the model of the Datalog database derived from  ... 
doi:10.1145/1455770.1455808 dblp:conf/ccs/OlsonGM08 fatcat:errpcb2nlfg5pjcps3bppsjaku

Relationlog: A typed extension to Datalog with sets and tuples

Mengchi Liu
1998 The Journal of Logic Programming  
which coincides with its model-theoretic semantics. © 1998 Elsevier Science Inc.  ...  It has been proved that extended relational algebra without the powerset operator and safe calculus without the subset predicate are equivalent [26] .  ...  Acknowledgements The author wishes to thank the anonymous referees for their detailed comments and suggestions which have significantly improved the quality and accuracy of the paper.  ... 
doi:10.1016/s0743-1066(98)00003-x fatcat:twjzhybvmfecnho2ny3pxv2etq

Tiresias

Alexandra Meliou, Dan Suciu
2012 Proceedings of the 2012 international conference on Management of Data - SIGMOD '12  
Tiresias generates the problem variables, constraints and objectives by issuing standard SQL statements, allowing for its integration with any RDBMS.  ...  How-To queries answer fundamental data analysis questions of the form: "How should the input change in order to achieve the desired output".  ...  We require the program to be stratified, in the sense that a rule having HP k in the head may only have the HDB's HP i with i < k in the body; HDB predicate may not be negated in the body.  ... 
doi:10.1145/2213836.2213875 dblp:conf/sigmod/MeliouS12 fatcat:v37orjkbpzgz5hqynjmqviztxq
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