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Galanaki, Chrysida.
Infinite-*game* *semantics* for logic programming languages.

Degree: 2014, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

URL: http://hdl.handle.net/10442/hedi/44078

This thesis focuses on the study of the semantics of logic programs and the development of infinite games of perfect information between two players that capture this semantics. Initially, we study propositional logic programming. In [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3 (1) (1986) 37-53] a game between two players is described. In this, given a propositional logic program without negation and a ground atom that belongs to the program, Player I, tries to prove that the atomic formula is true (he therefore has the role of the Believer), and the other that it is not (he therefore has the role of the Doubter). So the goal, succeeds as a result of a query to the program, if Player I has a winning strategy. In this thesis, the game is extended to capture the semantics of programs with negation. When during the game a negated atom appears, the two players switch roles. The Believer becomes Doubter and vice versa. In case of infinite role-switches we have a tie. It is proved that the game is determined. In the case of the game with three possible results, the game-theoretic semantics is equivalent to the well-founded semantics of the logic program. In order to prove that, we use a new refined game that has infinite possible outcomes. The value of that game depends on the number of role switches that take place during it. The refined game is also proved to be determined and its interpretation is a model of the program and equivalent to the infinite valued minimum model semantics as defined in [P.Rondogiannis,W.W.Wadge, Minimum model semantics for logic programs with negation-as-failure, ACM Transactions on Computational Logic 6(2)(2005) 441-467]. Our study then extends to the Intensional logic programming as presented in [M.A.Orgun, W.W.Wadge, Towards a unified theory of intensional logic programming, 13(4):413-440,1992] and is a generalization of temporal and modal logic programming. In order to capture the semantics of such languages we develop a new two-valued game of perfect information. This is also proved to be determined. The game interpretation is a model of the program and equivalent to the minimum model semantics defined by Orgun and Wadge. Subsequently, the game is extended so that it can allow role-switches between the two players, and that it has three possible outcomes (win for either Player I or Player II, or the two players tie). In that way, the game interpretation is proved to also capture the semantics of logic programs with negation or more generally any non-monotonic operator. This game semantics is the first semantic framework for non-monotonic intensional logic programming.

Η διατριβή επικεντρώνεται στη μελέτη της σημασιολογίας λογικών προγραμμάτων και την ανάπτυξη άπειρων παιγνίων πλήρους πληροφόρησης που αποδίδουν αυτή τη σημασιολογία. Αρχικώς, μελετάται ο προτασιακός λογικός προγραμματισμός. Στο άρθρο [M.H. van Emden, Quantitative deduction and its fixpoint theory, Journal of Logic Programming 3(1)(1986) 37-53] περιγράφεται ένα…

Subjects/Keywords: Λογικός προγραμματισμός; Παιγνιοθεωρητική σημασιολογία; Άπειρα παίγνια; Νοηματικός λογικός προγραμματισμός; Μη-μονοτονική συλλογιστική; Logic programming; Game-theoretic semantics; Infinite games; Intensional logic programming; Non-monotonic reasoning

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APA (6^{th} Edition):

Galanaki, C. (2014). Infinite-game semantics for logic programming languages. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/44078

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^{th} Edition):

Galanaki, Chrysida. “Infinite-game semantics for logic programming languages.” 2014. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed January 24, 2021. http://hdl.handle.net/10442/hedi/44078.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^{th} Edition):

Galanaki, Chrysida. “Infinite-game semantics for logic programming languages.” 2014. Web. 24 Jan 2021.

Vancouver:

Galanaki C. Infinite-game semantics for logic programming languages. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2014. [cited 2021 Jan 24]. Available from: http://hdl.handle.net/10442/hedi/44078.

Note: this citation may be lacking information needed for this citation format:

Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Galanaki C. Infinite-game semantics for logic programming languages. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2014. Available from: http://hdl.handle.net/10442/hedi/44078

Not specified: Masters Thesis or Doctoral Dissertation