40 research outputs found
Positive Dependency Graphs Revisited
Theory of stable models is the mathematical basis of answer set programming. Several results in that theory refer to the concept of the positive dependency graph of a logic program. We describe a modification of that concept and show that the new understanding of positive dependency makes it possible to strengthen some of these results
Counting Complexity for Reasoning in Abstract Argumentation
In this paper, we consider counting and projected model counting of
extensions in abstract argumentation for various semantics. When asking for
projected counts we are interested in counting the number of extensions of a
given argumentation framework while multiple extensions that are identical when
restricted to the projected arguments count as only one projected extension. We
establish classical complexity results and parameterized complexity results
when the problems are parameterized by treewidth of the undirected
argumentation graph. To obtain upper bounds for counting projected extensions,
we introduce novel algorithms that exploit small treewidth of the undirected
argumentation graph of the input instance by dynamic programming (DP). Our
algorithms run in time double or triple exponential in the treewidth depending
on the considered semantics. Finally, we take the exponential time hypothesis
(ETH) into account and establish lower bounds of bounded treewidth algorithms
for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1
Negation-as-failure considered harmful
In logic programs, negation-as-failure has been used both for representing negative information and for providing default nonmonotonic inference. In this paper we argue that this twofold role is not only unnecessary for the expressiveness of the language, but it also plays against declarative programming, especially if further negation symbols such as strong negation are also available. We therefore propose a new logic programming approach in which negation and default inference are independent, orthogonal concepts. Semantical characterization of this approach is given in the style of answer sets, but other approaches are also possible. Finally, we compare them with the semantics for logic programs with two kinds of negation.Red de Universidades con Carreras en Informática (RedUNCI
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A general approach to temporal reasoning about action and change
Reasoning about actions and change based on common sense knowledge is one of the most important and difficult tasks in the artificial intelligence research area. A series of such tasks are identified which motivate the consideration and application of reasoning formalisms. There follows a discussion of the broad issues involved in modelling time and constructing a logical language. In general, worlds change over time. To model the dynamic world, the ability to predict what the state of the world will be after the execution of a particular sequence of actions, which take time and to explain how some given state change came about, i.e. the causality are basic requirements of any autonomous rational agent.
The research work presented herein addresses some of the fundamental concepts and the relative issues in formal reasoning about actions and change. In this thesis, we employ a new time structure, which helps to deal with the so-called intermingling problem and the dividing instant problem. Also, the issue of how to treat the relationship between a time duration and its relative time entity is examined. In addition, some key terms for representing and reasoning about actions and change, such as states, situations, actions and events are formulated. Furthermore, a new formalism for reasoning about change over time is presented. It allows more flexible temporal causal relationships than do other formalisms for reasoning about causal change, such as the situation calculus and the event calculus. It includes effects that start during, immediately after, or some time after their causes, and which end before, simultaneously with, or after their causes. The presented formalism allows the expression of common-sense causal laws at high level. Also, it is shown how these laws can be used to deduce state change over time at low level. Finally, we show that the approach provided here is expressive
Modelling causal reasoning
PhDAlthough human causal reasoning is widely acknowledged as an object
of scientific enquiry, there is little consensus on an appropriate measure
of progress. Up-to-date evidence of the standard method of research in
the field shows that this method has been rejected at the birth of modern
science.
We describe an instance of the standard scientific method for modelling
causal reasoning (causal calculators). The method allows for uniform
proofs of three relevant computational properties: correctness of the model
with respect to the intended model, full abstraction of the model (function)
with respect to the equivalence of reasoning scenarios (input), and formal
relations of equivalence and subsumption between models. The method
extends and exploits the systematic paradigm [Handbook of Logic in Artificial
Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to
fit with our interpretation of it.
Using the described method, we present results for some major models,
with an updated summary spanning seventy-two years of research in the
field
Composition of hierarchic default specifications
[no abstract