There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We also prove (...) a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on paths (...) between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. Suggest reactive arrows to simplify the algorithms for the winning paths. We give a conceptual analysis of inheritance diagrams, and compare our analysis to the “small” and “big sets” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism of a particularly simple type. We show that the small and big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. We will also interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information. It is easily seen that inheritance diagrams can also be analysed in terms of reactive diagrams - as can all argumentation systems. AMS Classification: 68T27, 68T30. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...) which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to a definition of iaheritance that is..

One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. In light of our pervasive ignorance, we cannot get around in the world just reasoning deductively from our prior beliefs together with new perceptual input. As our conclusions are not guaranteed to be true, we must countenance the possibility that new information will lead us to change our minds, withdrawing previously adopted beliefs. In this sense, our (...) reasoning is “defeasible”. The question arises how defeasible reasoning works, or ought to work. In particular we need rules governing what a cognizer ought to believe given a set of interacting arguments some of which defeat others. That is what is called a “semantics” for defeasible reasoning, and this chapter will propose a new semantics that avoids certain clear counter-examples to all existing semantics. (shrink)