Supraclassical Consequence Relations - Tolerating Rare Counterexamples

A modal perspective on defeasible reasoning

We introduce various new supraclassical entailment relations for defeasible reasoning and investigate some of their relationships. The contrapositive of the usual nonmonotonic preferential entailment turns out to be a monotonic supraclassical entailment. Analogously to these two, a nonmonotonic and its contrapositive monotonic supraclassical entailment can be defined by using modal operators re...

Preservationist Logics and Nonmonotonic Logics

Any number of distinct logical consequence-relations can be represented in preservationist terms—as preserving one or more properties of sets of sentences—providing a general and abstract perspective from which to consider theories of consequence. One simple way of defining such consequence-relations, however, yields ones that are always strictly monotonic. At the same time, many nonmonotonic l...

Contractions of noncontractive Consequence Relations

Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relativ...

Model Exploration by Confidence with Completely Specified Counterexamples

We present an extensions of our previous work on axiomatizing confident general concept inclusions in given finite interpretations. Within this extension we allow external experts to interactively provide counterexamples to general concept inclusions with otherwise enough confidence in the given data. This extensions allows us to distinguish between erroneous counterexamples in the data and rar...

Supraclassical Inference without Probability