76 research outputs found
A New Rational Algorithm for View Updating in Relational Databases
The dynamics of belief and knowledge is one of the major components of any
autonomous system that should be able to incorporate new pieces of information.
In order to apply the rationality result of belief dynamics theory to various
practical problems, it should be generalized in two respects: first it should
allow a certain part of belief to be declared as immutable; and second, the
belief state need not be deductively closed. Such a generalization of belief
dynamics, referred to as base dynamics, is presented in this paper, along with
the concept of a generalized revision algorithm for knowledge bases (Horn or
Horn logic with stratified negation). We show that knowledge base dynamics has
an interesting connection with kernel change via hitting set and abduction. In
this paper, we show how techniques from disjunctive logic programming can be
used for efficient (deductive) database updates. The key idea is to transform
the given database together with the update request into a disjunctive
(datalog) logic program and apply disjunctive techniques (such as minimal model
reasoning) to solve the original update problem. The approach extends and
integrates standard techniques for efficient query answering and integrity
checking. The generation of a hitting set is carried out through a hyper
tableaux calculus and magic set that is focused on the goal of minimality.Comment: arXiv admin note: substantial text overlap with arXiv:1301.515
Arithmetical conservation results
In this paper we present a proof of Goodman's Theorem, a classical result in
the metamathematics of constructivism, which states that the addition of the
axiom of choice to Heyting arithmetic in finite types does not increase the
collection of provable arithmetical sentences. Our proof relies on several
ideas from earlier proofs by other authors, but adds some new ones as well. In
particular, we show how a recent paper by Jaap van Oosten can be used to
simplify a key step in the proof. We have also included an interesting
corollary for classical systems pointed out to us by Ulrich Kohlenbach
The -semantics approach; theory and applications
AbstractThis paper is a general overview of an approach to the semantics of logic programs whose aim is to find notions of models which really capture the operational semantics, and are, therefore, useful for defining program equivalences and for semantics-based program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (top-down) and a fixpoint (bottom-up) construction. It can also be characterized from the model-theoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version, and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semantics-based program transformation and analysis
The Computational Strength of Extensions of Weak Königâs Lemma
The weak König's lemma WKL is of crucial significance in the study of fragments of mathematics which on the one hand are mathematically strong but on the other hand have a low proof-theoretic and computational strength. In addition to the restriction to binary trees (or equivalently bounded trees), WKLis also `weak' in that the tree predicate is quantifier-free. Whereas in general the computational and proof-theoretic strength increases when logically more complex trees are allowed, we show that this is not the case for trees which aregiven by formulas in a class Phi where we allow an arbitrary function quantifier prefix over bounded functions in front of a Pi^0_1-formula. This results in a schema Phi-WKL.Another way of looking at WKL is via its equivalence to the principle For all x there exists y there exists
Specialization of Difference Equations and High Frobenius Powers
We study valued fields equipped with an automorphism which is
locally infinitely contracting in the sense that for
all . We show that various notions of valuation theory, such
as Henselian and strictly Henselian hulls, admit meaningful transformal
analogues. We prove canonical amalgamation results, and exhibit the way that
transformal wild ramification is controlled by torsors over generalized vector
groups. Model theoretically, we determine the model companion: it is decidable,
admits a simple axiomatization, and enjoys elimination of quantifiers up to
algebraically bounded quantifiers.
The model companion is shown to agree with the limit theory of the Frobenius
action on an algebraically closed and nontrivially valued field. This opens the
way to a motivic intersection theory for difference varieties that was
previously available only in characteristic zero. As a first consequence, the
class of algebraically closed valued fields equipped with a distinguished
Frobenius is decidable, uniformly in .Comment: identical to v1 apart from slight modifications in abstrac
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