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Automatic Strengthening of GraphStructured Knowledge Bases
"... ( † = corresponding author) We address two problems in underspecified graphstructured knowledge bases (GSKBs): the coreference and the provenance problem. Both problems are important for a variety of reasons. The former asks “Which existentially quantified variables in different but related axi ..."
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( † = corresponding author) We address two problems in underspecified graphstructured knowledge bases (GSKBs): the coreference and the provenance problem. Both problems are important for a variety of reasons. The former asks “Which existentially quantified variables in different but related axioms of a GSKB possibly denote identical domain individuals?”, and the latter “From which axioms in a GSKB is a piece of knowledge getting derived? ” To decide the former, we need to be able to prove equality between different variables – a GSKB in which this is possible is called a strenghtened GSKB, and an underspecified GSKB otherwise. The latter occur naturally in many knowledge acquisition contexts, and are also easier to author. We hence present an algorithm which rewrites an underspecified GSKB into a strengthened GSKB, by virtue of Skolemization and addition of equality atoms such that the coreference information can be drawn from it. This enlarges the logical theory (the deductive closure) of the GSKB and strengthens its inferential power, hence affecting the provenance information. Our algorithm is modeltheoretic in nature and exploits a novel class of desirable, preferred models, which capture the desired coreferences. The algorithm is a logical reconstruction of an implemented algorithm that we successfully applied to a largescale biological knowledge base, in which it identified more that 22,000 equality atoms. 1
On Extensions and Variants of Dependence Logic  A study of intuitionistic connectives in the team semantics setting
, 2014
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SPECIFICATIONS FOR DECIDABLE HYBRID AUTOMATA AND GAMES
, 2009
"... Using hybrid automata, one is able to model many types of systems and express their properties in various formal languages. Being extremely general and rich, however, the class of hybrid automata exhibits the inherent problems of automata theory: even the simplest of properties for general hybrid au ..."
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Using hybrid automata, one is able to model many types of systems and express their properties in various formal languages. Being extremely general and rich, however, the class of hybrid automata exhibits the inherent problems of automata theory: even the simplest of properties for general hybrid automata are undecidable. Therefore, one must restrict attention only to subclasses of this very general class. The literature to date has seemed to indicate that for a whole subclass of hybrid automata to have decidable properties it would either have to have very simple continuous dynamics (timed automata, piecewise affine inclusions, etc.) or decoupled discrete and continuous dynamics (ominimal hybrid systems, initialized rectangular automata), where the continuous components of the system are reset in a memoryless manner after each discrete transition. The thesis of this dissertation is that this need not be the case! STORMED hybrid systems are introduced in this dissertation and form a subclass of hybrid automata which lie on the boundary of decidability and admit
Distance Constraint Satisfaction Problems
, 2011
"... We study the complexity of constraint satisfaction problems for templates Γ that are firstorder definable in (Z; succ), the integers with the successor relation. In the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree), we show that Γ is homomorphically equivalent to a ..."
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We study the complexity of constraint satisfaction problems for templates Γ that are firstorder definable in (Z; succ), the integers with the successor relation. In the case that Γ is locally finite (i.e., the Gaifman graph of Γ has finite degree), we show that Γ is homomorphically equivalent to a structure with a certain majority polymorphism (which we call modular median) and the CSP for Γ can be solved in polynomial time, or Γ is homomorphically equivalent to a finite transitive structure, or the CSP for Γ is NPcomplete. Assuming a widely believed conjecture from finite domain constraint satisfaction (we require the tractability conjecture by Bulatov, Jeavons and Krokhin in the special case of transitive finite templates), this proves that those CSPs have a complexity dichotomy, that is, are either in P or NPcomplete. 1
A Partial Characterization of EhrenfeuchtFräısse ́ Games on Fields and Vector Spaces
, 2007
"... In this paper we examine EhrenfeuchtFräısse ́ (EF) games on fields and vector spaces. We find the exact length of the EF game on two algebraically closed fields of finite transcendence degree over Q or Z/pZ. We also determine an upper bound on the length of any EF game on models (Fn1,F1) and (F m ..."
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In this paper we examine EhrenfeuchtFräısse ́ (EF) games on fields and vector spaces. We find the exact length of the EF game on two algebraically closed fields of finite transcendence degree over Q or Z/pZ. We also determine an upper bound on the length of any EF game on models (Fn1,F1) and (F m 2,F2 of vector spaces where m = n and a lower bound for the special case F1 = F2. 1
Mutual SelfEvidence and Common Knowledge
, 2008
"... Epistemic game theory has shown how a commonality of beliefs can be maintained by a set of rational actors facing asymmetric information. The need for such commonality was stressed by Durkheim (1933 [1902]), who observed that the division of labor in modern society fosters a heterogeneous citizenry ..."
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Epistemic game theory has shown how a commonality of beliefs can be maintained by a set of rational actors facing asymmetric information. The need for such commonality was stressed by Durkheim (1933 [1902]), who observed that the division of labor in modern society fosters a heterogeneous citizenry and an ethic of individ