A modular translation from defeasible nets to defeasible logics

Abstract

The sceptical inheritance nets introduced in Horty et al. [Proceedings of AAAI-87 (1987):358-363] are translated into a version of Nute's defeasible logic. Moreover this translation is modular in the sense of Thomason and Horty [Non-Monotonic Reasoning. Springer-Verlag (1989):234]. Apart from the importance of relating two nonmonotonic reasoning formalisms, this result shows that the reasoning mechanisms underlying defeasible logic and defeasible nets are the same. Yet they were invented independently and set in totally different contexts. This is perhaps some evidence that the underlying nonmonotonic reasoning mechanism is mainly correct. We also observe that since defeasible logics can contain both absolute and defeasible rules, they provided a uniform setting for considering nets which contain both strict and defeasible arcs.     

谈判代理开发典型案例的研究

本文通过两个典型案例说明一个灵活有效的谈判代理开发方法.使用状态图和可废止逻辑规则说明谈判策略,将其动态地插入到一个集状态解释器和可废止逻辑推理引擎于一体的代理壳中,就可以获得所需要的自动谈判代理.由于状态图和可废止逻辑有很强的适应性,当应用环境发生变化时,只需调整其标准和规则的集合.     

Defeasible Logic on an Embedded Microcontroller

Defeasible logic is a system of reasoning in which rules have exceptions, and when rules conflict, the one that applies most specifically to the situation wins out. This paper reports a successful application of defeasible logic to the implementation of an embedded control system. The system was programmed in d-Prolog (a defeasible extension of Prolog), and the inferences were compiled into a truth table that was encoded on a low-end PIC microcontroller.Advantages of defeasible logic include conciseness and correct handling of the passage of time. It is distinct from fuzzy logic and probabilistic logic, addressing a different set of problems.     

The Control Layer in Open Mechanized Reasoning Systems: Annotations and Tactics

We are interested in developing a methodology for integrating mechanized reasoning systems such as Theorem Provers, Computer Algebra Systems, and Model Checkers. Our approach is to provide a framework for specifying mechanized reasoning systems and to use specifications as a starting point for integration. We build on the work presented by Giunchigliaet al. (1994) which introduces the notion of Open Mechanized Reasoning Systems (OMRS) as a specification framework for integrating reasoning systems. An OMRS specification consists of three components: the logic component, the control component, and the interaction component. In this paper we focus on the control level. We propose to specify the control component by first adding control knowledge to the data structures representing the logic by means of annotations and then by specifying proof strategies via tactics. To show the adequacy of the approach we present and discuss a structured specification of constraint contextual rewriting as a set of cooperating specialized reasoning modules.     

Reasoning about preferences in argumentation frameworks

The abstract nature of Dung's seminal theory of argumentation accounts for its widespread application as a general framework for various species of non-monotonic reasoning, and, more generally, reasoning in the presence of conflict. A Dung argumentation framework is instantiated by arguments and a binary conflict based attack relation, defined by some underlying logical theory. The justified arguments under different extensional semantics are then evaluated, and the claims of these arguments define the inferences of the underlying theory. To determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments. However, preference information is often itself defeasible, conflicting and so subject to argumentation. Hence, in this paper we extend Dung's theory to accommodate arguments that claim preferences between other arguments, thus incorporating meta-level argumentation based reasoning about preferences in the object level. We then define and study application of the full range of Dung's extensional semantics to the extended framework, and study special classes of the extended framework. The extended theory preserves the abstract nature of Dung's approach, thus aiming at a general framework for non-monotonic formalisms that accommodate defeasible reasoning about as well as with preference information. We illustrate by formalising argument based logic programming with defeasible priorities in the extended theory.     

Active logic semantics for a single agent in a static world

For some time we have been developing, and have had significant practical success with, a time-sensitive, contradiction-tolerant logical reasoning engine called the active logic machine (ALMA). The current paper details a semantics for a general version of the underlying logical formalism, active logic. Central to active logic are special rules controlling the inheritance of beliefs in general (and of beliefs about the current time in particular), very tight controls on what can be derived from direct contradictions ($P\mathrm{\&}\neg P$), and mechanisms allowing an agent to represent and reason about its own beliefs and past reasoning. Furthermore, inspired by the notion that until an agent notices that a set of beliefs is contradictory, that set seems consistent (and the agent therefore reasons with it as if it were consistent), we introduce an “apperception function” that represents an agent's limited awareness of its own beliefs, and serves to modify inconsistent belief sets so as to yield consistent sets. Using these ideas, we introduce a new definition of logical consequence in the context of active logic, as well as a new definition of soundness such that, when reasoning with consistent premises, all classically sound rules remain sound in our new sense. However, not everything that is classically sound remains sound in our sense, for by classical definitions, all rules with contradictory premises are vacuously sound, whereas in active logic not everything follows from a contradiction.     

An argumentation framework in default logic

This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more than revising an unstructural set of premises; rather it should be regarded as constructing and comparing arguments for incompatible conclusions. This point of view gives rise to two important observations, both pointing at some flaws of other theories. The first is that arguments should be compared as they are constructed, viz. step-by-step, while the second observation is that a knowledge representation language is needed with a defeasible conditional, since the material implication gives rise to arguments which are not constructed in actual reasoning. Accordingly, a nonmonotonic logic, default logic, is chosen as the formalism underlying the argumentation framework. The general structure of the framework allows for any standard for comparing pairs of arguments; in this study two such standards are investigated, based on specificity and on orderings of the premises.     

The universe of propositional approximations

The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249–310] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of propositional letters, approximates classical logic as the size of the set increases.     

Perceiving and Reasoning about a Changing World

A rational agent (artificial or otherwise) residing in a complex changing environment must gather information perceptually, update that information as the world changes, and combine that information with causal information to reason about the changing world. Using the system of defeasible reasoning that is incorporated into the OSCAR architecture for rational agents, a set of reason‐schemas is proposed for enabling an agent to perform some of the requisite reasoning. Along the way, solutions are proposed for the Frame Problem, the Qualification Problem, and the Ramification Problem. The principles and reasoning described have all been implemented in OSCAR.     

On Resolving Conflicts Between Arguments

Argument systems are based on the idea that one can construct arguments for propositions—structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of which (sub‐) arguments can be subject to defeat. In legal argumentation, metarules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, can a conflict be resolved by considering only the last defeasible rules of the arguments involved? We propose a new argument system where, instead of deriving a defeat relation between arguments, arguments for the defeat of defeasible rules are constructed. This system allows us to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, allows conflicts to be resolved using only the last rules of the arguments, allows us to establish a relation with Default Logic, and allows closure properties such as cumulativity to be proved. We propose an extension of the argument system based on a proposal for reasoning by cases in default logic.     

Abstract argumentation

In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the admissibility semantics for all these formalisms has a natural argumentation-theoretic interpretation and proof procedure, which seem to correspond well with informal argumentation.In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its non-provability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of non-provability claims.     

一种支持自治计算的基于可废止逻辑的柔性Agent

以自治计算的研究为背景,利用可废止逻辑理论的非单调知识表征和推理机制,提出一种能够动态接受规则变更、灵活处理实时发生的规则冲突,并进行高效的非单调推理的柔性Agent模型.这种Agent既是自主的,又是可控的,而且可以在开放、动态的环境中通过合同与其他Agent进行协同工作.     

ANGLE: An autonomous, normative and guidable agent with changing knowledge

Some emerging computing systems (especially autonomic computing systems) raise several challenges to autonomous agents, including (1) how to reflect the dynamics of business requirements, (2) how to coordinate with external agents with sufficient level of security and predictability, and (3) how to perform reasoning with dynamic and incomplete knowledge, including both informational knowledge (observations) and motivational knowledge (for example, policy rules and contract rules). On the basis of defeasible logic and argumentation, this paper proposes an autonomous, normative and guidable agent model, called ANGLE, to cope with these challenges. This agent is established by combining beliefs-desires-intentions (BDI) architecture with policy-based method and the mechanism of contract-based coordination. Its architecture, knowledge representation, as well as reasoning and decision-making, are presented in this paper. ANGLE is characteristic of the following three aspects. First, both its motivational knowledge and informational knowledge are changeable, and allowed to be incomplete, inconsistent/conflicting. Second, its knowledge is represented in terms of extended defeasible logic with modal operators. Different from the existing defeasible theories, its theories (including belief theory, goal theory and intention theory) are dynamic (called dynamic theories), reflecting the variations of observations and external motivational knowledge. Third, its reasoning and decision-making are based on argumentation. Due to the dynamics of underlying theories, argument construction is not a monotonic process, which is different from the existing argumentation framework where arguments are constructed incrementally.     

Probabilistic guarded commands mechanized in HOL

The probabilistic guarded-command language (pGCL) contains both demonic and probabilistic non-determinism, which makes it suitable for reasoning about distributed random algorithms. Proofs are based on weakest precondition semantics, using an underlying logic of real- (rather than Boolean-)valued functions.We present a mechanization of the quantitative logic for pGCL using the HOL theorem prover, including a proof that all pGCL commands satisfy the new condition sublinearity, the quantitative generalization of conjunctivity for standard GCL.The mechanized theory also supports the creation of an automatic proof tool which takes as input an annotated pGCL program and its partial correctness specification, and derives from that a sufficient set of verification conditions. This is employed to verify the partial correctness of the probabilistic voting stage in Rabin's mutual-exclusion algorithm.     

t-DeLP: an argumentation-based Temporal Defeasible Logic Programming framework

The aim of this paper is to propose an argumentation-based defeasible logic, called t-DeLP, that focuses on forward temporal reasoning for causal inference. We extend the language of the DeLP logical framework by associating temporal parameters to literals. A temporal logic program is a set of basic temporal facts and (strict or defeasible) durative rules. Facts and rules combine into durative arguments representing temporal processes. As usual, a dialectical procedure determines which arguments are undefeated, and hence which literals are warranted, or defeasibly follow from the program. t-DeLP, though, slightly differs from DeLP in order to accommodate temporal aspects, like the persistence of facts. The output of a t-DeLP program is a set of warranted literals, which is first shown to be non-contradictory and be closed under sub-arguments. This basic framework is then modified to deal with programs whose strict rules encode mutex constraints. The resulting framework is shown to satisfy stronger logical properties like indirect consistency and closure.     

Systemic approach to fuzzy logic formalization for approximate reasoning

L.A. Zadeh, E.H. Mamdani, M. Mizumoto, et al., R.A. Aliev and A. Tserkovny have proposed methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form “If x is A then y is B”, with A and B being fuzzy concepts (fuzzy sets). A formulation of fuzzy antecedent/consequent chains is one of the most important topics within a wide spectrum of problems in fuzzy sets in general and approximate reasoning, in particular. From the analysis of relevant research it becomes clear that for this purpose, a so-called fuzzy conditional inference rules comes as a viable alternative. In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. For this reason, we put together some comparative analysis of fuzzy reasoning methods in which antecedents contain a conditional proposition with fuzzy concepts and which are based on implication operators present in various types of fuzzy logic. We also show a process of a formation of the fuzzy logic regarded as an algebraic system closed under all its operations. We examine statistical characteristics of the proposed fuzzy logic. As the matter of practical interest, we construct a set of fuzzy conditional inference rules on the basis of the proposed fuzzy logic. Continuity and stability features of the formalized rules are investigated.     

Default logic and specification of nonmonotonic reasoning

In this paper constructions leading to the formation of belief sets by agents are studied. The focus is on the situation when possible belief sets are built incrementally in stages. An infinite sequence of theories that represents such a process is called a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper a generalization of default logic of Reiter is introduced by allowing infinite sets of justifications. This formalism is called infinitary default logic. In the main result of the paper it is shown that every reasoning frame can be represented by an infinitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.