Complete Axiomatizations of Fragments of Monadic Second-Order Logic on Finite Trees

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations of the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable

Queries with Guarded Negation (full version)

A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical algorithms in the case of unions of conjunctive queries, but become difficult or even undecidable when queries are allowed to contain negation. Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation. We introduce a fragment of SQL, called GN-SQL, as well as a fragment of Datalog with stratified negation, called GN-Datalog, that allow only guarded negation, and we show that these query languages are computationally well behaved, in terms of testing query containment, query evaluation, open-world query answering, and boundedness. GN-SQL and GN-Datalog subsume a number of well known query languages and constraint languages, such as unions of conjunctive queries, monadic Datalog, and frontier-guarded tgds. In addition, an analysis of standard benchmark workloads shows that most usage of negation in SQL in practice is guarded negation

From weak to strong types of LE1L_E^1-convergence by the Bocce-criterion

Necessary and sufficient oscillation conditions are given for a weakly convergent sequence (resp. relatively weakly compact set) in the Bochner-Lebesgue space \l1 to be norm convergent (resp. relatively norm compact), thus extending the known results for \rl1. Similarly, necessary and sufficient oscillation conditions are given to pass from weak to limited (and also to Pettis-norm) convergence in \l1. It is shown that tightness is a necessary and sufficient condition to pass from limited to strong convergence. Other implications between several modes of convergence in \l1 are also studied

Remarks on Nash equilibria for games with additively coupled payoffs (revision, previous title: An unusual Nash equilibrium result and its application to games with allocations in infinite dimensions)

If the payoffs of a game are affine, then they are additively coupled. In this situation both the Weierstrass theorem and the Bauer maximum principle can be used to produce existence results for a Nash equilibrium, since each player is faced with an individual, independent optimization problem. We consider two instances in the literature where these simple observations immediately lead to substantial generalizations

More on maximum likelihood equilibria for games with random payoffs and participation

Maximum likelihood Nash equilibria were introduced by Borm et al. (1995) for games with nitely many players and random payos. In Voorneveld (1999) random participation was added to the model. These existence results were extended by Balder (2000c) to continuum games with random payos and participation. However, in that paper the complicated measurability issue for the central equilibrium likelihood notion was bypassed by using inner probabilities for the central equilibrium likelihood notion. Here those measurability questions are shown to have a quite satisfactory resolution; this makes the maximum likelihood equilibrium notion more natural. Our main results are not only more general than those found in Borm et al. (1995) and Voorneveld (1999), but also improve upon them

The partition semantics of questions, syntactically

Groenendijk and Stokhof (1984, 1996; Groenendijk 1999) provide a logically attractive theory of the semantics of natural language questions, commonly referred to as the partition theory. Two central notions in this theory are entailment between questions and answerhood. For example, the question "Who is going to the party?" entails the question "Is John going to the party?", and "John is going to the party" counts as an answer to both. Groenendijk and Stokhof define these two notions in terms of partitions of a set of possible worlds. We provide a syntactic characterization of entailment between questions and answerhood . We show that answers are, in some sense, exactly those formulas that are built up from instances of the question. This result lets us compare the partition theory with other approaches to interrogation -- both linguistic analyses, such as Hamblin's and Karttunen's semantics, and computational systems, such as Prolog. Our comparison separates a notion of answerhood into three aspects: equivalence (when two questions or answers are interchangeable), atomic answers (what instances of a question count as answers), and compound answers (how answers compose).Comment: 14 page

On characterizing optimality and existence of optimal solutions for Lyapunov type optimization problems

Necessary and sucient conditions for optimality, in the form of a duality result of Fritz-John type, are given for an abstract optimization problem of Lyapunov type. The introduction of a so-called integrand constraint qualication allows the duality result to take the form of a Kuhn-Tucker type result. Special applications include necessary and sucient conditions for the existence of optimal controls for certain optimal control problems