9,984 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
Do Hard SAT-Related Reasoning Tasks Become Easier in the Krom Fragment?
Many reasoning problems are based on the problem of satisfiability (SAT).
While SAT itself becomes easy when restricting the structure of the formulas in
a certain way, the situation is more opaque for more involved decision
problems. We consider here the CardMinSat problem which asks, given a
propositional formula and an atom , whether is true in some
cardinality-minimal model of . This problem is easy for the Horn
fragment, but, as we will show in this paper, remains -complete (and
thus -hard) for the Krom fragment (which is given by formulas in
CNF where clauses have at most two literals). We will make use of this fact to
study the complexity of reasoning tasks in belief revision and logic-based
abduction and show that, while in some cases the restriction to Krom formulas
leads to a decrease of complexity, in others it does not. We thus also consider
the CardMinSat problem with respect to additional restrictions to Krom formulas
towards a better understanding of the tractability frontier of such problems
Reasoning about Explanations for Negative Query Answers in DL-Lite
In order to meet usability requirements, most logic-based applications
provide explanation facilities for reasoning services. This holds also for
Description Logics, where research has focused on the explanation of both TBox
reasoning and, more recently, query answering. Besides explaining the presence
of a tuple in a query answer, it is important to explain also why a given tuple
is missing. We address the latter problem for instance and conjunctive query
answering over DL-Lite ontologies by adopting abductive reasoning; that is, we
look for additions to the ABox that force a given tuple to be in the result. As
reasoning tasks we consider existence and recognition of an explanation, and
relevance and necessity of a given assertion for an explanation. We
characterize the computational complexity of these problems for arbitrary,
subset minimal, and cardinality minimal explanations
Generalized trapezoidal words
The factor complexity function of a finite or infinite word
counts the number of distinct factors of of length for each .
A finite word of length is said to be trapezoidal if the graph of its
factor complexity as a function of (for ) is
that of a regular trapezoid (or possibly an isosceles triangle); that is,
increases by 1 with each on some interval of length , then
is constant on some interval of length , and finally
decreases by 1 with each on an interval of the same length . Necessarily
(since there is one factor of length , namely the empty word), so
any trapezoidal word is on a binary alphabet. Trapezoidal words were first
introduced by de Luca (1999) when studying the behaviour of the factor
complexity of finite Sturmian words, i.e., factors of infinite "cutting
sequences", obtained by coding the sequence of cuts in an integer lattice over
the positive quadrant of made by a line of irrational slope.
Every finite Sturmian word is trapezoidal, but not conversely. However, both
families of words (trapezoidal and Sturmian) are special classes of so-called
"rich words" (also known as "full words") - a wider family of finite and
infinite words characterized by containing the maximal number of palindromes -
studied in depth by the first author and others in 2009.
In this paper, we introduce a natural generalization of trapezoidal words
over an arbitrary finite alphabet , called generalized trapezoidal
words (or GT-words for short). In particular, we study combinatorial and
structural properties of this new class of words, and we show that, unlike the
binary case, not all GT-words are rich in palindromes when , but we can describe all those that are rich.Comment: Major revisio
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