2,280 research outputs found
Semiring Provenance for Büchi Games: Strategy Analysis with Absorptive Polynomials
No full textThis paper presents a case study for the application of semiring semantics for fixed-point formulae to the analysis of strategies in Büchi games. Semiring semantics generalizes the classical Boolean semantics by permitting multiple truth values from certain semirings. Evaluating the fixed-point formula that defines the winning region in a given game in an appropriate semiring of polynomials provides not only the Boolean information on who wins, but also tells us how they win and which strategies they might use. This is well-understood for reachability games, where the winning region is definable as a least fixed point. The case of Büchi games is of special interest, not only due to their practical importance, but also because it is the simplest case where the fixed-point definition involves a genuine alternation of a greatest and a least fixed point. We show that, in a precise sense, semiring semantics provide information about all absorption-dominant strategies -- strategies that win with minimal effort, and we discuss how these relate to positional and the more general persistent strategies. This information enables applications such as game synthesis or determining minimal modifications to the game needed to change its outcome. Lastly, we discuss limitations of our approach and present questions that cannot be immediately answered by semiring semantics
Locality Theorems in Semiring Semantics
No full textSemiring semantics of first-order logic generalises classical Boolean semantics by permitting truth values from a commutative semiring, which can model information such as costs or access restrictions. This raises the question to what extent classical model-theoretic properties still apply, and how this depends on the algebraic properties of the semiring.
In this paper, we study this question for the classical locality theorems due to Hanf and Gaifman. We prove that Hanf’s locality theorem generalises to all semirings with idempotent operations, but fails for many non-idempotent semirings. We then consider Gaifman normal forms and show that for formulae with free variables, Gaifman’s theorem does not generalise beyond the Boolean semiring. Also for sentences, it fails in the natural semiring and the tropical semiring. Our main result, however, is a constructive proof of the existence of Gaifman normal forms for min-max and lattice semirings. The proof implies a stronger version of Gaifman’s classical theorem in Boolean semantics: every sentence has a Gaifman normal form which does not add negations
Semiring Provenance in the Infinite
No full textSemiring provenance evaluates database queries or logical statements not just by true or false but by values in some commutative semiring. This permits to track which combinations of atomic facts are responsible for the truth of a statement, and to derive further information, for instance concerning costs, confidence scores, number of proof trees, or access levels to protected data. The focus of this approach, proposed and developed to a large extent by Val Tannen and his collaborators, has first been on (positive) database query languages, but has later been extended, again in collaboration with Val, to a systematic semiring semantics for first-order logic (and other logical systems), as well as to a method for the strategy analysis of games.
So far, semiring provenance has been studied for finite structures. To extend the semiring provenance approach for first-order logic to infinite domains, the semirings need to be equipped with addition and multiplication operators over infinite collections of values. This needs solid algebraic foundations, and we study here the necessary and desirable properties of semirings with infinitary operations to provide a well-defined and informative provenance analysis over infinite domains. We show that, with suitable definitions for such infinitary semiring, large parts of the theory of semiring provenance can be succesfully generalised to infinite structures
Logic and Random Discrete Structures (Dagstuhl Seminar 22061)
No full textThis report documents the program and the outcomes of Dagstuhl Seminar 22061 "Logic and Random Discrete Structures". The main topic of this seminar has been the analysis of large random discrete structures, such as trees, graphs, or permutations, from the perspective of mathematical logic. It has brought together both experts and junior researchers from a number of different areas where logic and random structures play a role, with the goal to establish new connections between such areas and to encourage interactions between foundational research and different application areas, including probabilistic databases
Semiring Provenance for Fixed-Point Logic
No full textSemiring provenance is a successful approach, originating in database theory, to providing detailed information on how atomic facts combine to yield the result of a query. In particular, general provenance semirings of polynomials or formal power series provide precise descriptions of the evaluation strategies or "proof trees" for the query. By evaluating these descriptions in specific application semirings, one can extract practical information for instance about the confidence of a query or the cost of its evaluation.
This paper develops semiring provenance for very general logical languages featuring the full interaction between negation and fixed-point inductions or, equivalently, arbitrary interleavings of least and greatest fixed points. This also opens the door to provenance analysis applications for modal μ-calculus and temporal logics, as well as for finite and infinite model-checking games.
Interestingly, the common approach based on Kleene’s Fixed-Point Theorem for ω-continuous semirings is not sufficient for these general languages. We show that an adequate framework for the provenance analysis of full fixed-point logics is provided by semirings that are (1) fully continuous, and (2) absorptive. Full continuity guarantees that provenance values of least and greatest fixed-points are well-defined. Absorptive semirings provide a symmetry between least and greatest fixed-points and make sure that provenance values of greatest fixed points are informative.
We identify semirings of generalized absorptive polynomials S^{∞}[X] and prove universal properties that make them the most general appropriate semirings for our framework. These semirings have the further property of being (3) chain-positive, which is responsible for having truth-preserving interpretations that give non-zero values to all true formulae. We relate the provenance analysis of fixed-point formulae with provenance values of plays and strategies in the associated model-checking games. Specifically, we prove that the provenance value of a fixed point formula gives precise information on the evaluation strategies in these games
Matthias Wagner : author profile
No full textThe author presented on this page has published his 10. article in Angewandte Chemie in the last 10 years
Enduring Ambiguity: What Is European Literature? Matthias Nawrat in Conversation with Monika Woltig
No full textMatthias Nawrat is a Polish-German author living in Germany born in Opole, Poland. He moved with his family to Bamberg in 1989. He was awarded the Adelbert-von-ChamissoFörderpreis, was nominated for the Deutscher Buchpreis, received the Bremen Literature Prize and the Alfred Döblin Medaille. His most important novels were "Wir zwei allein" (2012), "Die vielen Tode unseres Opas Jurek" (2015), and "Der traurige Gast" (2019).Matthias Nawrat to niemiecki autor polskiego pochodzenia. Matthias Nawrat urodził się w Opolu i wraz z rodziną przeprowadził się w 1989 roku do Bambergu. Uzyskał Nagrodę im. Adelberta von Chamisso (Förderpreis), był nominowany do Niemieckiej Nagrody Książkowej (Deutscher Buchpreis), otrzymał Nagrodę Literacką miasta Bremy i Medal im. Alfreda Döblina. Najważniejsze teksty: "Wir zwei allein" (2012), "Die vielen Tode unseres Opas Jurek" (2015), "Der traurige Gast" (2019).Matthias Nawrat ist ein deutscher Autor polnischer Herkunft. Matthias Nawrat wurde im polnischen Opole geboren und siedelte 1989 mit seiner Familie nach Bamberg über. Er wurde mit dem Adelbert-von-Chamisso-Förderpreis ausgezeichnet, zum Deutschen Buchpreis nominiert und erhielt den Bremer Literaturpreis sowie die Alfred-Döblin-Medaille. Die wichtigsten Texte: "Wir zwei allein" (2012), "Die vielen Tode unseres Opas Jurek" (2015), "Der traurige Gast" (2019)
Baculus Militaris Compendiosus Infanterie Oder Officirers Stab Das ist Ein kurtzer Begrieff der Kriegs Lectionen bey dem Fußvolck gebräuchlich auch nötig : Bestehend in sechserley Exercitien 1. In der Partisan, halber Pique oder Jägerstock. 2. In der Fahn. 3. In der Pique. 4. In der Musqueten. 5. In der Musqueten mit der gabel oben und unten mit einer eiserner spitzen und in der mitten mit einem ein geschrobenen hacken. 6. In Hieb degen/ welcher bey dem fußvolck brauchlich / [Matthias Schlüter]
No full textJohn Matthias
No full textPoster promoting author John Matthias reading from his work in the Auditorium, Building 9, University of North Florida.
Poster dimensions: 26.7 cm x 41.8 cmhttps://digitalcommons.unf.edu/performances_print/1013/thumbnail.jp
Patristical Ideas in the Works of Matthias of Janov
No full textANGLICKÁ ANOTACE Title: Patristical ideas in the works of Matthias of Janov The thesis treats of the identification of ideas of church fathers in the work and thinking of Matthias of Janov. The thesis consits of three main parts. First part deals with Matthias of Janov in broader context of church tradition. Major political and theological developments that could have an impact on Matthias theological work are presented in this section. Second part introduces life of Matthias of Janov and identifies his major theological contributions. In the third part of the thesis, following explanation of methodology used, the findings of the author are presented. Three areas were selected by the author and researched in view of the identification of possible influance of church fathers in the Matthias of Janov work: the idea of Antichrist, frequent eucharisty and condemnation of idolatry. The findings confirm a strong influance of Augustin and Hieronymus in particular and other early church fathers on the formation of the theology of Matthias of Janov in all three areas of the study. It was also noticed that through the church fathers Matthias of Janov was strongly influenced by neoplatonism which was documented on his idea of "The First Thruth" Key words: Matthias of Janov, church fathers, antichrist, eucharisty,..
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