Steven Kutsch

Regular and Sufficient Bounds of Finite Domain Constraints for Skeptical C-Inference

Skeptical c-inference based on a set of conditionals of the form If A then usually B is defined by taking the set of c-representations into account. C-representations are ranking functions induced by impact vectors encoding the conditional impact on each possible world. By setting a bound for the maximal impact value, c-inference can be approximated. We investigate the concepts of regular and sufficient upper bounds for conditional impacts and how they can be employed for implementing c-inference as a finite domain constraint solving problem.

A Practical Comparison of Qualitative Inferences with Preferred Ranking Models

When reasoning qualitatively from a conditional knowledge base, two established approaches are system Z and p-entailment. The latter infers skeptically over all ranking models of the knowledge base, while system Z uses the unique pareto-minimal ranking model for the inference relations. Between these two extremes of using all or just one ranking model, the approach of c-representations generates a subset of all ranking models with certain constraints. Recent work shows that skeptical inference over all c-representations of a knowledge base includes and extends p-entailment. In this paper, we follow the idea of using preferred models of the knowledge base instead of the set of all models as a base for the inference relation. We employ different minimality constraints for c-representations and demonstrate inference relations from sets of preferred c-representations with respect to these constraints. We present a practical tool for automatic c-inference that is based on a high-level, declarative constraint-logic programming approach. Using our implementation, we illustrate that different minimality constraints lead to inference relations that differ mutually as well as from system Z and p-entailment.

Properties of skeptical c-inference for conditional knowledge bases and its realization as a constraint satisfaction problem

While the axiomatic system P is an important standard for plausible, nonmonotonic inferences from conditional knowledge bases, it is known to be too weak to solve benchmark problems like Irrelevance or Subclass Inheritance. Ordinal conditional functions provide a semantic base for system P and have often been used to design stronger inference relations, like Pearl’s system Z, or c-representations. While each c-representation shows excellent inference properties and handles particularly Irrelevance and Subclass Inheritance properly, it is still an open problem which c-representation is the best. In this paper, we consider the skeptical inference relation, called c-inference, that is obtained by taking all c-representations of a given knowledge base into account. We study properties of c-inference and show in particular that it preserves the properties of solving Irrelevance and Subclass Inheritance. Based on a characterization of c-representations as solutions of a Constraint Satisfaction Problem (CSP), we also model skeptical c-inference as a CSP and prove soundness and completeness of the modelling, ensuring that constraint solvers can be used for implementing c-inference.

Comparison of Inference Relations Defined over Different Sets of Ranking Functions

Skeptical inference in the context of a conditional knowledge base \(\mathcal R\) can be defined with respect to a set of models of \(\mathcal R\). For the semantics of ranking functions that assign a degree of surprise to each possible world, we develop a method for comparing the inference relations induced by different sets of ranking functions. Using this method, we address the problem of ensuring the correctness of approximating c-inference for \(\mathcal R\) by constraint satisfaction problems (CSPs) over finite domains. While in general, determining a sufficient upper bound for these CSPs is an open problem, for a sequence of simple knowledge bases investigated only experimentally before, we prove that using the number of conditionals in \(\mathcal R\) as an upper bound correctly captures skeptical c-inference.

Compilation of Conditional Knowledge Bases for Computing C-Inference Relations

A conditional knowledge base \(\mathcal {R}\) contains defeasible rules of the form “If A, then usually B”. For the notion of c-representations, a skeptical inference relation taking all c-representations of \(\mathcal {R}\) into account has been suggested. In this paper, we propose a 3-phase compilation scheme for both knowledge bases and skeptical queries to constraint satisfaction problems. In addition to skeptical c-inference, we show that also credulous and weakly skeptical c-inference can be modelled as a constraint satisfaction problem, and that the compilation scheme can be extended to such queries. For each compilation step, we prove its soundness and completeness, and demonstrate significant efficiency benefits when querying the compiled version of \(\mathcal {R}\). These findings are also supported by experiments with the software system InfOCF that employs the proposed compilation scheme.

Computation and comparison of nonmonotonic skeptical inference relations induced by sets of ranking models for the realization of intelligent agents

Skeptical inference of an intelligent agent in the context of a knowledge base R

System Z FO : Default reasoning with system Z-like ranking functions for unary first-order conditional knowledge bases

\mathcal {R}

Skeptical, Weakly Skeptical, and Credulous Inference Based on Preferred Ranking Functions.

containing conditionals of the form If A then usually B can be defined with respect to a set of models of R

Minimal Tolerance Pairs for System Z-Like Ranking Functions for First-Order Conditional Knowledge Bases.

\mathcal {R}

From Concepts in Non-Monotonic Reasoning to High-Level Implementations Using Abstract State Machines and Functional Programming.

. For the semantics of ranking functions that assign a degree of surprise to each possible world, we develop a method for comparing the inference relations induced by different sets of ranking models. Using this method, we address the problem of ensuring the correctness of approximating skeptical c-inference for R