nonmonotonic reasoning


Modeling Uncertainty and Imprecision in Nonmonotonic Reasoning using Fuzzy Numbers

arXiv.org Artificial Intelligence

Modern applications of artificial intelligence in decision support systems, plan generation systems require reasoning with imprecise a nd uncertain information. Logical frameworks based on bivalent reasoning are not suitable for such applications, because the set {0, 1} cannot capture the vagueness or uncertainty of underlying proposition. Though fuzzy log ic-based systems can represent imprecise linguistic information by ascribi ng membership values to attributes (or truth values to propositions) taken fr om the interval 1 [0,1], but this graded valuation becomes inadequate if the p recise membership can not be determined due to some underlying uncerta inty. This uncertainty may arise from lack of complete information or f rom lack of reliability of source of information or lack of unanimity amon g rational agents in a multi-agent reasoning system or from many other reasons . This uncertainty with respect to the assignment of membership degr ees is captured by assigning a range of possible membership values, i.e. by a ssigning an interval.


Nonmonotonic Reasoning

Journal of Artificial Intelligence Research

Nonmonotonic reasoning concerns situations when information is incomplete or uncertain. Thus, conclusions drawn lack iron-clad certainty that comes with classical logic reasoning. New information, even if the original one is retained, may change conclusions. Formal ways to capture mechanisms involved in nonmonotonic reasoning, and to exploit them for computation as in the answer set programming paradigm are at the heart of this research area. The six papers accepted for the special track contain significant contributions to the foundations of logic programming under the answer set semantics, to nonmonotonic extensions of description logics, to belief change in restricted settings, and to argumentation.


A Unified Framework for Nonmonotonic Reasoning with Vagueness and Uncertainty

arXiv.org Artificial Intelligence

Answer set programming (ASP) is a declarative problem solvi ng paradigm for nonmonotonic reasoning. ASP allows intuitiive represe ntation of combinatorial search and optimization problems and is widely use d for knowledge representation and reasoning in various applications like plan generation, natural language processing etc [14, 15]. But ASP can not dea l with fuzzy information, where attributes and truth degrees lie in a con tinuous range of values. Fuzzy Answer Set Programming (F ASP) is proposed as a n extension of ASP that allows graded truth values from the interval [0,1 ]. Theoretical advancement of F ASP is remarkable [18, 32, 9, 22, 23].


Applications of Linear Defeasible Logic: combining resource consumption and exceptions to energy management and business processes

arXiv.org Artificial Intelligence

Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine sub-structural features, corresponding to the consumption of resources, with defeasibility aspects to handle potentially conflicting information, has been discussed in literature, by some of the authors. Two applications emerged that are very relevant: energy management and business process management. We illustrate a set of guide lines to determine how to apply linear defeasible logic to those contexts.


About epistemic negation and world views in Epistemic Logic Programs

arXiv.org Artificial Intelligence

In this paper we consider Epistemic Logic Programs, which extend Answer Set Programming (ASP) with "epistemic operators" and "epistemic negation", and a recent approach to the semantics of such programs in terms of World Views. We propose some observations on the existence and number of world views. We show how to exploit an extended ASP semantics in order to: (i) provide a characterization of world views, different from existing ones; (ii) query world views and query the whole set of world views.


A Unified Algebraic Framework for Non-Monotonicity

arXiv.org Artificial Intelligence

Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much called for. In this paper, we present an algebraic graded logic we refer to as LogAG capable of encompassing a wide variety of non-monotonic formalisms. We build on Lin and Shoham's argument systems first developed to formalize non-monotonic commonsense reasoning. We show how to encode argument systems as LogAG theories, and prove that LogAG captures the notion of belief spaces in argument systems. Since argument systems capture default logic, autoepistemic logic, the principle of negation as failure, and circumscription, our results show that LogAG captures the before-mentioned non-monotonic logical formalisms as well. Previous results show that LogAG subsumes possibilistic logic and any non-monotonic inference relation satisfying Makinson's rationality postulates. In this way, LogAG provides a powerful unified framework for non-monotonicity.


On Rational Monotony and Weak Rational Monotony for Inference Relations Induced by Sets of Minimal C-Representations

AAAI Conferences

Reasoning in the context of a conditional knowledge base containing rules of the form ’If A then usually B’ can be defined in terms of preference relations on possible worlds. These preference relations can be modeled by ranking functions that assign a degree of disbelief to each possible world. In general, there are multiple ranking functions that accept a given knowledge base. Several nonmonotonic inference relations have been proposed using c-representations, a subset of all ranking functions. These inference relations take subsets of all c-representations based on various notions of minimality into account, and they operate in different inference modes, i.e., skeptical, weakly skeptical, or credulous. For nonmonotonic inference relations, weaker versions of monotonicity like rational monotony (RM) and weak rational monotony (WRM) have been developed. In this paper, we investigate which of the inference relations induced by sets of minimal c-representations satisfy rational monotony or weak rational monotony.


A reconstruction of the multipreference closure

arXiv.org Artificial Intelligence

The paper describes a preferential approach for dealing with exceptions in KLM preferential logics, based on the rational closure. It is well known that the rational closure does not allow an independent handling of the inheritance of different defeasible properties of concepts. Several solutions have been proposed to face this problem and the lexicographic closure is the most notable one. In this work, we consider an alternative closure construction, called the Multi Preference closure (MP-closure), that has been first considered for reasoning with exceptions in DLs. Here, we reconstruct the notion of MP-closure in the propositional case and we show that it is a natural variant of Lehmann's lexicographic closure. Abandoning Maximal Entropy (an alternative route already considered but not explored by Lehmann) leads to a construction which exploits a different lexicographic ordering w.r.t. the lexicographic closure, and determines a preferential consequence relation rather than a rational consequence relation. We show that, building on the MP-closure semantics, rationality can be recovered, at least from the semantic point of view, resulting in a rational consequence relation which is stronger than the rational closure, but incomparable with the lexicographic closure. We also show that the MP-closure is stronger than the Relevant Closure.


Optimizing Answer Set Computation via Heuristic-Based Decomposition

arXiv.org Artificial Intelligence

Answer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and nonmonotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP system DLV, in particular into its grounding subsystem I-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal. Under consideration in Theory and Practice of Logic Programming (TPLP).


Towards Lazy Grounding with Lazy Normalization in Answer-Set Programming — Extended Abstract

AAAI Conferences

Answer-Set Programming (ASP) is an expressive rule-based knowledge-representation formalism supported by efficient solver technology. Traditional evaluation of answer-set programs takes place in two phases: grounding and solving. Grounding incurs an up-to exponential increase in space, termed the grounding bottleneck of ASP, which is often encountered in practice. Lazy grounding avoids this bottleneck but is restricted to normal rules, significantly limiting the expressive power of this approach. We propose a framework to handle aggregates by normalizing them on demand during the lazy grounding process; we call this approach lazy normalization. It is feasible for different types of aggregates and can bring about up-to exponential gains in space and time.