scholarly journals Complexity of Prioritized Default Logics

1998 ◽  
Vol 9 ◽  
pp. 423-461 ◽  
Author(s):  
J. Rintanen
Keyword(s):  
Computational Complexity ◽  
Default Logic ◽  
Default Reasoning ◽  
Polynomial Hierarchy ◽  
Inference Mechanism ◽  
Default Rules ◽  
Computational Properties ◽  
Default Logics

In default reasoning, usually not all possible ways of resolving conflicts between default rules are acceptable. Criteria expressing acceptable ways of resolving the conflicts may be hardwired in the inference mechanism, for example specificity in inheritance reasoning can be handled this way, or they may be given abstractly as an ordering on the default rules. In this article we investigate formalizations of the latter approach in Reiter's default logic. Our goal is to analyze and compare the computational properties of three such formalizations in terms of their computational complexity: the prioritized default logics of Baader and Hollunder, and Brewka, and a prioritized default logic that is based on lexicographic comparison. The analysis locates the propositional variants of these logics on the second and third levels of the polynomial hierarchy, and identifies the boundary between tractable and intractable inference for restricted classes of prioritized default theories.

Constrained Epistemic Extension on Agent Knowledge Acquisition

2013 ◽  
Vol 651 ◽  
pp. 943-948
Author(s):  
Zhi Ling Hong ◽  
Mei Hong Wu
Keyword(s):  
Epistemic Logic ◽  
Information Acquisition ◽  
Default Logic ◽  
Dynamic Epistemic Logic ◽  
Default Reasoning ◽  
Multi Agent Systems ◽  
Negotiation Strategy ◽  
Agent Systems ◽  
Multi Agent ◽  
Default Rules

In multi-agent systems, a number of autonomous pieces of software (the agents) interact in order to execute complex tasks. This paper proposes a logic framework portrays agent’s communication protocols in the multi-agent systems and a dynamic negotiation model based on epistemic default logic was introduced in this framework. In this paper, we use the constrained default rules to investigate the extension of dynamic epistemic logic, and constrained epistemic extension construct an efficient negotiation strategy via constrained epistemic default reasoning, which guarantees the important natures of extension existence and semi-monotonicity. We also specify characteristic of the dynamic updating when agent learn new knowledge in the logical framework. The method for the information sharing signify the usefulness of logical tools carried out in the dynamic process of information acquisition, and the distributed intelligent information processing show the effectiveness of reasoning default logic in the dynamic epistemic logic theory.

scholarly journals STATISTICAL INFERENCE AS DEFAULT REASONING

1999 ◽  
Vol 13 (02) ◽  
pp. 267-283 ◽  
Author(s):  
HENRY E. KYBURG ◽  
CHOH MAN TENG
Keyword(s):  
Statistical Inference ◽  
Statistical Test ◽  
Default Logic ◽  
Default Reasoning ◽  
Default Rules

Classical statistical inference is nonmonotonic in nature. We show how it can be formalized in the default logic framework. The structure of statistical inference is the same as that represented by default rules. In particular, the prerequisite corresponds to the sample statistics, the justifications require that we do not have any reason to believe that the sample is misleading, and the consequence corresponds to the conclusion sanctioned by the statistical test.

A tutorial on default reasoning

1998 ◽  
Vol 13 (3) ◽  
pp. 225-246 ◽  
Author(s):  
GRIGORIS ANTONIOU
Keyword(s):  
Computational Models ◽  
Default Logic ◽  
Default Reasoning ◽  
Default Rules

Default reasoning is concerned with making inferences in cases where the information at hand is incomplete. In such cases it is necessary to make plausible assumptions, which in default reasoning are based on default rules. This paper gives an introduction to the field. It discusses in depth one particular approach, default logic, including properties, semantics and computational models. It also gives an overview of other ideas and approaches.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

Default Reasoning for Forensic Visual Surveillance Based on Subjective Logic and its Comparison with L-Fuzzy Set Based Approaches

2013 ◽  
pp. 51-94
Author(s):  
Seunghan Han ◽  
Walter Stechele
Keyword(s):  
Fuzzy Set ◽  
Default Logic ◽  
Visual Surveillance ◽  
Default Reasoning ◽  
Illustrative Case ◽  
Reasoning Under Uncertainty ◽  
Subjective Logic ◽  
Continuous Space ◽  
Uncertainty Handling ◽  
Belief Theory

Default reasoning can provide a means of deriving plausible semantic conclusion under imprecise and contradictory information in forensic visual surveillance. In such reasoning under uncertainty, proper uncertainty handling formalism is required. A discrete species of Bilattice for multivalued default logic demonstrated default reasoning in visual surveillance. In this article, the authors present an approach to default reasoning using subjective logic that acts in a continuous space. As an uncertainty representation and handling formalism, subjective logic bridges Dempster Shafer belief theory and second order Bayesian, thereby making it attractive tool for artificial reasoning. For the verification of the proposed approach, the authors extend the inference scheme on the bilattice for multivalued default logic to L-fuzzy set based logics that can be modeled with continuous species of bilattice structures. The authors present some illustrative case studies in visual surveillance scenarios to contrast the proposed approach with L-fuzzy set based approaches.

scholarly journals Beyond NP: Quantifying over Answer Sets

2019 ◽  
Vol 19 (5-6) ◽  
pp. 705-721
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA ◽  
MIROSLAW TRUSZCZYNSKI
Keyword(s):  
Answer Set Programming ◽  
The Other ◽  
Polynomial Hierarchy ◽  
Programming Paradigm ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
The One ◽  
Image Position ◽  
Answer Sets ◽  
Computational Properties

AbstractAnswer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling problems beyond NP with ASP is known to be complicated, on the one hand, and limited to problems in $\[\Sigma _2^P\]$ on the other. Inspired by the way Quantified Boolean Formulas extend SAT formulas to model problems beyond NP, we propose an extension of ASP that introduces quantifiers over stable models of programs. We name the new language ASP with Quantifiers (ASP(Q)). In the paper we identify computational properties of ASP(Q); we highlight its modeling capabilities by reporting natural encodings of several complex problems with applications in artificial intelligence and number theory; and we compare ASP(Q) with related languages. Arguably, ASP(Q) allows one to model problems in the Polynomial Hierarchy in a direct way, providing an elegant expansion of ASP beyond the class NP.

scholarly journals Bosons vs. Fermions – A computational complexity perspective

2021 ◽  
Vol 43 (suppl 1) ◽  
Author(s):  
Daniel Jost Brod
Keyword(s):  
Computational Complexity ◽  
Complexity Theory ◽  
Undergraduate Students ◽  
Quantum Systems ◽  
Polynomial Hierarchy ◽  
Complexity Classes ◽  
Computational Power ◽  
Linear Optics ◽  
Computational Complexity Theory ◽  
Classical Computer

Recent years have seen a flurry of activity in the fields of quantum computing and quantum complexity theory, which aim to understand the computational capabilities of quantum systems by applying the toolbox of computational complexity theory. This paper explores the conceptually rich and technologically useful connection between the dynamics of free quantum particles and complexity theory. I review results on the computational power of two simple quantum systems, built out of noninteracting bosons (linear optics) or noninteracting fermions. These rudimentary quantum computers display radically different capabilities—while free fermions are easy to simulate on a classical computer, and therefore devoid of nontrivial computational power, a free-boson computer can perform tasks expected to be classically intractable. To build the argument for these results, I introduce concepts from computational complexity theory. I describe some complexity classes, starting with P and NP and building up to the less common #P and polynomial hierarchy, and the relations between them. I identify how probabilities in free-bosonic and free-fermionic systems fit within this classification, which then underpins their difference in computational power. This paper is aimed at graduate or advanced undergraduate students with a Physics background, hopefully serving as a soft introduction to this exciting and highly evolving field.

scholarly journals A Note on the Asymptotics and Computational Complexity of Graph Distinguishability

10.37236/1361 ◽  
1998 ◽  
Vol 5 (1) ◽  
Author(s):  
Alexander Russell ◽  
Ravi Sundaram
Keyword(s):  
Computational Complexity ◽  
Polynomial Hierarchy ◽  
Distinguishing Number

A graph $G$ is said to be $d$-distinguishable if there is a $d$-coloring of $G$ which no non-trivial automorphism preserves. That is, $\exists \chi: G \rightarrow \{1, \ldots, d\},$ $$ \forall \phi \in \mathrm{Aut}(G) \setminus \{\mathbf{id}\}, \exists v, \chi(v) \neq \chi(\phi(v)). $$ It was conjectured that if $|G| > |\mathrm{Aut}(G)|$ and the $\mathrm{Aut}(G)$ action on $G$ has no singleton orbits, then $G$ is 2-distinguishable. We give an example where this fails. We partially repair the conjecture by showing that when "enough motion occurs," the distinguishing number does indeed decay. Specifically, defining $$ {\mathrm{m} }(G) = \min_{{\phi \in \mathrm{Aut}(G)} \atop {\phi \neq \mathbf{id}}} |\{v \in G \;:\;\phi(v) \neq v\}|, $$ we show that when ${\mathrm{m}}(G) > 2\log_2 |\mathrm{Aut}(G)|$, $G$ is 2-distinguishable. In general, we show that if $ {\mathrm{m}}(G)\ln d > 2\ln |\mathrm{Aut}(G)|$ then $G$ is $d$-distinguishable. There has been considerable interest in the computational complexity of the $d$-distinguishability problem. Specifically, there has been much musing on the computational complexity of the language $$ \{(G, d)\; : \; G \text{ is $d$-distinguishable}\}. $$ We show that this language lies in AM $\subset \Sigma_2^P \cap \Pi_2^P$. We use this to conclude that if Dist is $\mathbf{coNP}$-hard then the polynomial hierarchy collapses.

scholarly journals Reasoning About Prescription and Description Using Prioritized Default Rules

10.29007/swdn ◽  
2018 ◽  
Author(s):  
Valentin Cassano ◽  
Carlos Areces ◽  
Pablo Castro
Keyword(s):  
Software Engineering ◽  
Deontic Logic ◽  
Default Logic ◽  
Logical Framework ◽  
Standard Deontic Logic ◽  
Default Rules

In this paper we introduce a prioritized default logic. We build this logic modularly from Standard Deontic Logic by the addition of default rules and priorities among them. Our main aim is to provide a logical framework to reason about scenarios where prescriptive and descriptive statements coexist and may be incomplete and contradictory. We motivate and illustrate the technical elements of our work with the use of examples (classical, and coming from software engineering). In addition, we present sound, complete, and terminating (with loop check) tableau-based proof calculi for credulous and sceptical reasoning in our logic.

Sign in / Sign up

Export Citation Format

Share Document