On a rule-based interpretation of default conditionals

In nonmonotonic reasoning, a default conditional α→β has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. There is however an alternative interpretation, in which a default is regarded essentially as a rule, leading from premises to conclusion. In this paper, we present a family of logics, based on this alternative interpretation. A general semantic framework under this rule-based interpretation is developed, and associated proof theories for a family of weak conditional logics is specified. Nonmonotonic inference is easily defined in these logics. Interestingly, the logics presented here are weaker than the commonly-accepted base conditional approach for defeasible reasoning. However, this approach resolves problems that have been associated with previous approaches.      

On the complexity of extension checking in default logic

The complexity of deciding equivalence of a formula to an extension of a default theory is investigated for the Reiter, justified, constrained, and rational semantics.     

Modelling default and likelihood reasoning as probabilistic reasoning

This paper presents a probabilistic analysis of plausible reasoning about defaults and about likelihood. Likely and by default are in fact treated as duals in the same sense as possibility and necessity. To model these four forms probabilistically, a logicQDP and its quantitative counterpartDP are derived that allow qualitative and corresponding quantitative reasoning. Consistency and consequence results for subsets of the logics are given that require at most a quadratic number of satisfiability tests in the underlying prepositional logic. The quantitative logic shows how to track the propagation error inherent in these reasoning forms. The methodology and sound framework of the system highlights their approximate nature, the dualities, and the need for complementary reasoning about relevance.Much of this research was done while at the University of Technology, Sydney, Broadway, NSW, Australia, and some at the Turing Institute, 36 Nth. Hanover Str., Glasgow, Scotland.     

Outlier detection for simple default theories

It was noted recently that the framework of default logics can be exploited for detecting outliers. Outliers are observations expressed by sets of literals that feature unexpected properties. These observations are not explicitly provided in input (as it happens with abduction) but, rather, they are hidden in the given knowledge base. Unfortunately, in the two related formalisms for specifying defaults — Reiter's default logic and extended disjunctive logic programs — the most general outlier detection problems turn out to lie at the third level of the polynomial hierarchy. In this note, we analyze the complexity of outlier detection for two very simple classes of default theories, namely NU and DNU, for which the entailment problem is solvable in polynomial time. We show that, for these classes, checking for the existence of an outlier is anyway intractable. This result contributes to further showing the inherent intractability of outlier detection in default reasoning.     

High-probabilities,model-preference and default arguments

In this paper we analyze two recent conditional interpretations of defaults, one based on probabilities, and the other, on models. We study what makes them equivalent, explore their limitations and develop suitable extensions. The resulting framework ties together a number of important notions in default reasoning, like high-probabilities and model-preference, default priorities and argument systems, and independence assumptions and minimality considerations.I want to thank D. Nute and J. Pearl for comments on an earlier version of this paper.     

Modal logic for default reasoning

In the paper we introduce a variant of autoepistemic logic that is especially suitable for expressing default reasonings. It is based on the notion of iterative expansion. We show a new way of translating default theories into the language of modal logic under which default extensions correspond exactly to iterative expansions. Iterative expansions have some attractive properties. They are more restrictive than autoepistemic expansions, and, for some classes of theories, than moderately grounded expansions. At the same time iterative expansions avoid several undesirable properties of strongly grounded expansions, for example, they are grounded in the whole set of the agent's initial assumptions and do not depend on their syntactic representation.Iterative expansions are defined syntactically. We define a semantics which leads to yet another notion of expansion — weak iterative expansion — and we show that there is an important class of theories, that we call -programs, for which iterative and weak iterative expansions coincide. Thus, for -programs, iterative expansions can be equivalently defined by semantic means.This work was partially supported by Army Research Office under grant DAAL03-89-K-0124, and by National Science Foundation and the Commonwealth of Kentucky EPSCoR program under grant RII 8610671.     

Yet some more complexity results for default logic

We identify several new tractable subsets and several new intractable simple cases for reasoning in the propositional version of Reiter's default logic. The majority of our findings are related to brave reasoning. By making some intuitive observations, most classes that we identify can be derived quite easily from some subsets of default logic already known in the literature. Some of the subsets we discuss are subclasses of the so-called “extended logic programs”. All the tractable subsets presented in this paper can be recognized in linear time.     

An approach to fuzzy default reasoning for function approximation

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions     

The Dynamics of Syntactic Knowledge

The syntactic approach to epistemic logic avoids the logicalomniscience problem by taking knowledge as primary rather thanas defined in terms of possible worlds. In this study, we combinethe syntactic approach with modal logic, using transition systemsto model reasoning. We use two syntactic epistemic modalities:‘knowing at least’ a set of formulae and ‘knowingat most’ a set of formulae. We are particularly interestedin models restricting the set of formulae known by an agentat a point in time to be finite. The resulting systems are investigatedfrom the point of view of axiomatization and complexity. Weshow how these logics can be used to formalise non-omniscientagents who know some inference rules, and study their relationshipto other systems of syntactic epistemic logics, such as Ågotnesand Walicki (2004, Proc. 2nd EUMAS, pp. 1–10), Alechinaet al. (2004, Proc. 3rd AAMAS, pp. 601–613), Duc (1997,J. Logic Comput., 7, 633–648).     

Reasoning about reasoning in a meta-level architecture

In this paper we discuss reasoning about reasoning in a multiple agent scenario. We consider agents that are perfect reasoners, loyal, and that can take advantage of both the knowledge and ignorance of other agents. The knowledge representation formalism we use is (full) first order predicate calculus, where different agents are represented by different theories, and reasoning about reasoning is realized via a meta-level representation of knowledge and reasoning. The framework we provide is pretty general: we illustrate it by showing a machine checked solution to the three wisemen puzzle. The agents' knowledge is organized into units: the agent's own knowledge about the world and its knowledge about other agents are units containing object-level knowledge; a unit containing meta-level knowledge embodies the reasoning about reasoning and realizes the link among units. In the paper we illustrate the meta-level architecture we propose for problem solving in a multi-agent scenario; we discuss our approach in relation to the modal one and we compare it with other meta-level architectures based on logic. Finally, we look at a class of applications that can be effectively modeled by exploiting the meta-level approach to reasoning about knowledge and reasoning.     

认识逻辑(1):关于知识和信念的逻辑框架

知识和信念是人工智能领域研究中经常涉及到的两个重要概念。本文讨论了知识和信念的涵义与关系,定义了认识逻辑系统ＥＩ,讨论了它的语法和语义,证明了认识逻辑ＥＬ不但是可靠的而且是完备的,认为逻辑ＥＬ不但可以用来描述人类的认识过程,还可以用于对常识推理以及分布式系统的形式化描述。     

基于动态描述逻辑DDL的动作理论

基于一阶谓词逻辑或高阶逻辑的动作理论与采用命题语言的动作理论之间存在一个关于描述和推理能力的鸿沟;作为描述逻辑的动态扩展,动态描述逻辑DDL为基于描述逻辑的动作刻画和推理提供了一种途径.系统地研究了基于DDL的动作表示和推理问题.首先,在应用描述逻辑对静态领域知识进行刻画的基础上,引入带参数的原子动作定义式和带参数的复...     

Reasoning about Minimal Knowledge in Nonmonotonic Modal Logics

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms.