A state-based knowledge representation approach for information logical inconsistency detection in warning systems

Detecting logical inconsistency in collected information is a vital function when deploying a knowledge-based warning system to monitor a specific application domain for the reason that logical inconsistency is often hidden from seemingly consistent information and may lead to unexpected results. Existing logical inconsistency detection methods usually focus on information stored in a knowledge base by using a well-defined general purpose knowledge representation approach, and therefore cannot fulfill the demands of a domain-specific situation. This paper first proposes a state-based knowledge representation approach, in which domain-specific knowledge is expressed by combinations of the relevant objects’ states. Based on this approach, a method for information logical inconsistency detection (ILID) is developed which can flexibly handle the demands of various domain-specific situations through reducing part of restrictions in existing methods. Finally, two real-case based examples are presented to illustrate the ILID method and its advantages.     

A logic for reasoning with inconsistency

Most known computational approaches to reasoning have problems when facing inconsistency, so they assume that a given logical system is consistent. Unfortunately, the latter is difficult to verify and very often is not true. It may happen that addition of data to a large system makes it inconsistent, and hence destroys the vast amount of meaningful information. We present a logic, called APC (annotated predicate calculus; cf. annotated logic programs of [4, 5]), that treats any set of clauses, either consistent or not, in a uniform way. In this logic, consequences of a contradiction are not nearly as damaging as in the standard predicate calculus, and meaningful information can still be extracted from an inconsistent set of formulae. APC has a resolution-based sound and complete proof procedure. We also introduce a novel notion of epistemic entailment and show its importance for investigating inconsistency in predicate calculus as well as its application to nonmonotonic reasoning. Most importantly, our claim that a logical theory is an adequate model of human perception of inconsistency, is actually backed by rigorous arguments.A preliminary report on this research appeared in LICS'89.Work of M. Kifer was supported in part by the NSF grants DCR-8603676, IRI-8903507.Work of E. L. Lozinskii was supported in part by Israel National Council for Research and Development under the grants 2454-3-87, 2545-2-87, 2545-3-89 and by Israel Academy of Science, grant 224-88.     

Nonmonotonic inconsistency

Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and a series of results showing that nonmonotonic inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence.The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all.     

Reasoning composite beliefs using a qualitative approach

A Bayesian network is a knowledge representation technique for use in expert system development. The probabilistic knowledge encoded in a Bayesian network is a set of composite hypotheses expressed over the permutation of a set of variables (propositions). Ordering these composite hypotheses according to their a posteriori probabilities can be exponentially hard. This paper presents a qualitative reasoning approach which takes advantage of certain types of topological structures and probability distributions of a Bayesian network to derive the partial ordering of composite hypotheses. Such an approach offers an attractive alternative to reduce the computational complexity of deriving a partial ordering in which consistency is guaranteed.This work is supported in part by a grant to Queens College from the General Research Branch, National Institute of Health under grant No. RR-07064.     

A fixed-parameter algorithm for minimum quartet inconsistency

Given n taxa, exactly one topology for every subset of four taxa, and a positive integer k (the parameter), the Minimum Quartet Inconsistency (MQI) problem is the question whether we can find an evolutionary tree inducing a set of quartet topologies that differs from the given set in only k quartet topologies. The more general problem where we are not necessarily given a topology for every subset of four taxa appears to be fixed-parameter intractable. For MQI, however, which is also NP-complete, we can compute the required tree in time O(4^kn+n⁴). This means that the problem is fixed-parameter tractable and that in the case of a small number k of “errors” the tree reconstruction can be done efficiently. In particular, for minimal k, our algorithm can produce all solutions that resolve k errors. Additionally, we discuss significant heuristic improvements. Experiments underline the practical relevance of our solutions.     

System LS: A Three-Tiered Nonmonotonic Reasoning System

In this paper, a formal system of nonmonotonic reasoning is developed, which takes as its inspiration the manner in which some people make logically justifiable conclusions about nonmonotonic reasoning problems. The people, when asked about individuals, compare the logical strength of the arguments relating any sets to which the individual belongs, to other sets. A three-tiered system of rules including rules of System P as well as Transitivity and Monotonicity is developed. The system, known as System LS for logical strength, deals with three levels of non-strict relationships:

• α ₁β  α are normally β ( more than half of the α are β ) ;

       
  
  

A frequentist approach to mapping under uncertainty

An asynchronous stochastic approximation based (frequentist) approach is proposed for mapping using noisy mobile sensors under two different scenarios: (1) perfectly known sensor locations and (2) uncertain sensor locations. The frequentist methodology has linear complexity in the map components, is immune to the data association problem and is provably consistent. The frequentist methodology, in conjunction with a Bayesian estimator, is applied to the Simultaneous Localization and Mapping (SLAM) problem of Robotics. Several large maps are estimated using the hybrid Bayesian/Frequentist scheme and results show that the technique is robust to the computational and performance issues inherent in the purely Bayesian approaches to the problem.     

A full invariant under dynamic output feedback: a generalizedinverse approach

A novel full invariant of linear time-invariant multivariable systems under causal dynamic output feedback is derived. It makes use of a generalized inverse approach     

The Wonham filter under uncertainty: A game–theoretic approach

The paper is devoted to a state filtering problem of Markov jump processes given the continuous and/or counting observations. All the transition intensity matrix, observation plan and counting intensity are parameterized by a random vector with uncertain distribution on a known support set.The estimation problem is formulated in minimax settings with a conditional optimality criterion. We reduce the initial minimax problem to a dual problem of constrained quadratic optimization. The corresponding numerical algorithm of minimax filtering is presented as well as its illustrative implementation in the monitoring of a TCP link status under uncertainty.     

Measuring inconsistency in knowledgebases

It is well-known that knowledgebases may contain inconsistencies. We provide a measure to quantify the inconsistency of a knowledgebase, thereby allowing for the comparison of the inconsistency of various knowledgebases, represented as first-order logic formulas. We use quasi-classical (QC) logic for this purpose. QC logic is a formalism for reasoning and analysing inconsistent information. It has been used as the basis of a framework for measuring inconsistency in propositional theories. Here we extend this framework, by using a first-order logic version of QC logic for measuring inconsistency in first-order theories. We motivate the QC logic approach by considering some formulae as database or knowledgebase integrity constraints. We then define a measure of extrinsic inconsistency that can be used to compare the inconsistency of different knowledgebases. This measure takes into account both the language used and the underlying domain. We show why this definition also captures the intrinsic inconsistency of a knowledgebase. We also provide a formalization of paraconsistent equality, called quasi-equality, and we use this in an extended example of an application for measuring inconsistency between heterogeneous sources of information and integrity constraints prior to merging.     

A section is born: Studies in Automated Reasoning

A section is born: Studies in Automated Reasoning     

Reasoning about Knowledge: A Response by the Authors

Minds and Machines -     

Symbolical Reasoning about Numerical Data: A Hybrid Approach

By combining methods from artificial intelligence and signal analysis, we have developed a hybrid system for medical diagnosis. The core of the system is a fuzzy expert system with a dual source knowledge base. Two sets of rules are acquired, automatically from given examples and indirectly formulated by the physician. A fuzzy neural network serves to learn from sample data and allows to extract fuzzy rules for the knowledge base. A complex signal transformation preprocesses the digital data a priori to the symbolic representation. Results demonstrate the high accuracy of the system in the field of diagnosing electroencephalograms where it outperforms the visual diagnosis by a human expert for some phenomena.     

Perceptual Reasoning for Perceptual Computing: A Similarity-Based Approach

Perceptual reasoning (PR) is an approximate reasoning method that can be used as a computing-with-words (CWW) engine in perceptual computing. There can be different approaches to implement PR, e.g., firing-interval-based PR (FI-PR), which has been proposed in J. M. Mendel and D. Wu, IEEE Trans. Fuzzy Syst., vol. 16, no. 6, pp. 1550–1564, Dec. 2008 and similarity-based PR (S-PR), which is proposed in this paper. Both approaches satisfy the requirement on a CWW engine that the result of combining fired rules should lead to a footprint of uncertainty (FOU) that resembles the three kinds of FOUs in a CWW codebook. A comparative study shows that S-PR leads to output FOUs that resemble word FOUs, which are obtained from subject data, much more closely than FI-PR; hence, S-PR is a better choice for a CWW engine than FI-PR.      

一个有效的加权不精确推理算法

本文针对医疗诊断推理的难点,给出了一个借助矩阵的变换来实现推理的不精确推理算法,并通过实例解释了算法的推理过程;该算法考虑了规则中命题的权重、规则的可信度,表现出良好的适应性.     

Design of optimal control under uncertain initial conditions: A minimax approach

The need for a game-theoretical formulation of the problem of linear-quadratic control under nonmeasurable plant state where the functional depends on the uncertain initial state was substantiated. The minimax output control law in terms of linear matrix inequalities that may be regarded as the optimal robust control law for the given set of the plant initial states was established assuming that the measurable components of the initial state were known and the nonmeasurable components take on values within the given ellipsoid. The results obtained were generalized to the plants with uncertain parameters.     

Negation as inconsistency. I

The notion of negation as inconsistency is motivated and introduced into PROLOG. This negation is fully compatible with classical negation and gives a version of PROLOG which is a stronger fragment of classical logic than ordinary PROLOG. It is intended that negation as inconsistency replace the notion of negation as failure. Negation as inconsistency can be generalized in a natural way and in its generalized form will include negation as failure as a special case.