The Expressive Power of Higher-order Datalog: An XSB Implementation

Η πτυχιακή εργασία ακολουθεί τα αποτελέσματα του μη δημοσιευμένου ακόμα άρθρου των, Α. Χαραλαμπίδη, Χ. Νομικού και Π. Ροντογιάννη με τίτλο “The Expressive Power of Higher-order Datalog”. Το άρθρο παρουσιάζει μία απόδειξη ισοδυναμίας σε εκφραστική ισχύ της Datalog υψηλής-τάξης, με τις χρονικά εκθετικά περιορισμένες μηχανές Turing. Με άλλα λόγια ότι η Datalog υψηλής-τάξης εκφράζει τις κλάσεις πολυπλοκότητας των προβλημάτων απόφασης EXP^(k)TIME. Η πτυχιακή εργασία αυτή, θα παρουσιάσει με λεπτομέρεια τα παραπάνω αποτελέσματα, καθώς και θα υποδείξει κάποια σφάλματα στα προγράμματα που αναγράφονται στο άρθρο, καθώς και θα προτείνει τρόπους επίλυσής τους. Επιπλέον θα παρατεθεί μία λειτουργική υλοποίηση των προγραμμάτων στο σύστημα XSB, με στόχο την τεκμηρίωση των παραπάνω αποτελεσμάτων.This thesis follows the results in the yet unpublished paper of A. Charalambidis, Ch. Nomikos and P. Rondogiannis namely “The Expressive Power of Higher-order Datalog”. That paper proposes a proof which shows that Higher-order Datalog is equivalent in computational power to exponentially time bounded Turing Machines. In other words that higher-order Datalog captures the complexity class of decision problems EXP^(k)TIME. This thesis will review the above result in detail while demonstrating and proposing solutions for the flaws in the programs written in that paper. In addition a working implementation of the programs in the XSB system will be provided which shows that the proposed results hold

Datalog with Negation and Monotonicity

Positive Datalog has several nice properties that are lost when the language is extended with negation. One example is that fixpoints of positive Datalog programs are robust w.r.t. the order in which facts are inserted, which facilitates efficient evaluation of such programs in distributed environments. A natural question to ask, given a (stratified) Datalog program with negation, is whether an equivalent positive Datalog program exists. In this context, it is known that positive Datalog can express only a strict subset of the monotone queries, yet the exact relationship between the positive and monotone fragments of semi-positive and stratified Datalog was previously left open. In this paper, we complete the picture by showing that monotone queries expressible in semi-positive Datalog exist which are not expressible in positive Datalog. To provide additional insight into this gap, we also characterize a large class of semi-positive Datalog programs for which the dichotomy `monotone if and only if rewritable to positive Datalog\u27 holds. Finally, we give best-effort techniques to reduce the amount of negation that is exhibited by a program, even if the program is not monotone

On relating CTL to Datalog

CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTL -- we prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs.Comment: 34 pages, 1 figure (file .eps

Rewritability in Monadic Disjunctive Datalog, MMSNP, and Expressive Description Logics

We study rewritability of monadic disjunctive Datalog programs, (the complements of) MMSNP sentences, and ontology-mediated queries (OMQs) based on expressive description logics of the ALC family and on conjunctive queries. We show that rewritability into FO and into monadic Datalog (MDLog) are decidable, and that rewritability into Datalog is decidable when the original query satisfies a certain condition related to equality. We establish 2NExpTime-completeness for all studied problems except rewritability into MDLog for which there remains a gap between 2NExpTime and 3ExpTime. We also analyze the shape of rewritings, which in the MMSNP case correspond to obstructions, and give a new construction of canonical Datalog programs that is more elementary than existing ones and also applies to formulas with free variables