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Inference with System W Satisfies Syntax Splitting

arXiv.org Artificial Intelligence

In this paper, we investigate inductive inference with system W from conditional belief bases with respect to syntax splitting. The concept of syntax splitting for inductive inference states that inferences about independent parts of the signature should not affect each other. This was captured in work by Kern-Isberner, Beierle, and Brewka in the form of postulates for inductive inference operators expressing syntax splitting as a combination of relevance and independence; it was also shown that c-inference fulfils syntax splitting, while system P inference and system Z both fail to satisfy it. System W is a recently introduced inference system for nonmonotonic reasoning that captures and properly extends system Z as well as c-inference. We show that system W fulfils the syntax splitting postulates for inductive inference operators by showing that it satisfies the required properties of relevance and independence. This makes system W another inference operator besides c-inference that fully complies with syntax splitting, while in contrast to c-inference, also extending rational closure.


Descriptor Revision for Conditionals: Literal Descriptors and Conditional Preservation

arXiv.org Artificial Intelligence

Descriptor revision by Hansson is a framework for addressing the problem of belief change. In descriptor revision, different kinds of change processes are dealt with in a joint framework. Individual change requirements are qualified by specific success conditions expressed by a belief descriptor, and belief descriptors can be combined by logical connectives. This is in contrast to the currently dominating AGM paradigm shaped by Alchourr\'on, G\"ardenfors, and Makinson, where different kinds of changes, like a revision or a contraction, are dealt with separately. In this article, we investigate the realisation of descriptor revision for a conditional logic while restricting descriptors to the conjunction of literal descriptors. We apply the principle of conditional preservation developed by Kern-Isberner to descriptor revision for conditionals, show how descriptor revision for conditionals under these restrictions can be characterised by a constraint satisfaction problem, and implement it using constraint logic programming. Since our conditional logic subsumes propositional logic, our approach also realises descriptor revision for propositional logic.


Axiomatic Evaluation of Epistemic Forgetting Operators

AAAI Conferences

Forgetting as a knowledge management operation has received much less attention than operations like inference, or revision. It was mainly in the area of logic programming that techniques and axiomatic properties have been studied systematically. However, at least from a cognitive view, forgetting plays an important role in restructuring and reorganizing a human's mind, and it is closely related to notions like relevance and independence which are crucial to knowledge representation and reasoning. In this paper, we propose axiomatic properties of (intentional) forgetting for general epistemic frameworks which are inspired by those for logic programming, and we evaluate various forgetting operations which have been proposed recently by Beierle et al. according to them. The general aim of this paper is to advance formal studies of (intentional) forgetting operators while capturing the many facets of forgetting in a unifying framework in which different forgetting operators can be contrasted and distinguished by means of formal properties.


Rational Inference Patterns Based on Conditional Logic

AAAI Conferences

Conditional information is an integral part of representation and inference processes of causal relationships, temporal events, and even the deliberation about impossible scenarios of cognitive agents. For formalizing these inferences, a proper formal representation is needed. Psychological studies indicate that classical, monotonic logic is not the approriate model for capturing human reasoning: There are cases where the participants systematically deviate from classically valid answers, while in other cases they even endorse logically invalid ones. Many analyses covered the independent analysis of individual inference rules applied by human reasoners. In this paper we define inference patterns as a formalization of the joint usage or avoidance of these rules. Considering patterns instead of single inferences opens the way for categorizing inference studies with regard to their qualitative results. We apply plausibility relations which provide basic formal models for many theories of conditionals, nonmonotonic reasoning, and belief revision to asses the rationality of the patterns and thus the individual inferences drawn in the study. By this replacement of classical logic with formalisms most suitable for conditionals, we shift the basis of judging rationality from compatibility with classical entailment to consistency in a logic of conditionals. Using inductive reasoning on the plausibility relations we reverse engineer conditional knowledge bases as explanatory model for and formalization of the background knowledge of the participants. In this way the conditional knowledge bases derived from the inference patterns provide an explanation for the outcome of the study that generated the inference pattern.


Nonmonotonic Inferences with Qualitative Conditionals based on Preferred Structures on Worlds

arXiv.org Artificial Intelligence

A conditional knowledge base R is a set of conditionals of the form "If A, the usually B". Using structural information derived from the conditionals in R, we introduce the preferred structure relation on worlds. The preferred structure relation is the core ingredient of a new inference relation called system W inference that inductively completes the knowledge given explicitly in R. We show that system W exhibits desirable inference properties like satisfying system P and avoiding, in contrast to e.g. system Z, the drowning problem. It fully captures and strictly extends both system Z and skeptical c-inference. In contrast to skeptical c-inference, it does not require to solve a complex constraint satisfaction problem, but is as tractable as system Z.