An assurance case provides a structured argument to establish a claim for a system based on evidence about the system and its environment. I propose a simple interpretation for the overall argument that uses epistemic methods for its evidential or leaf steps and logic for its reasoning or interior steps: evidential steps that cross some threshold of credibility are accepted as premises in a cla...

This paper studies learning inference by induction. We first consider the problem of learning logical inference rules. Given a set S of propositional formulas and their logical consequences T , the goal is to find deductive inference rules that produce T from S. We show that an induction algorithm LF1T, which learns logic programs from interpretation transitions, successfully produces deductive...

The LF logical framework codifies a methodology for representing deductive systems, such as programming languages and logics, within a dependently typed λ-calculus. In this methodology, the syntactic and deductive apparatus of a system is encoded as the canonical forms of associated LF types; an encoding is correct (adequate) if and only if it defines a compositional bijection between the appar...

Vague predicates such as heap, tall, bald, near to, nicer than, etc. are characterized by their Sorites susceptibility and the existence of borderline cases. In attempting to develop a general theory, diverse vague predicates are often analyzed in rather broad natural language settings. Because this has proven to be rather difficult, the phenomenon of vagueness is studied here in a narrower and...

In the context of the cognitive study of diagrammatic representations for deductive reasoning, the availability of syntactic manipulation of diagrams has played a key role in accounting for their efficacy. Currently, however, little has been known about the interface between such syntactic or proof-theoretical aspects and the corresponding semantic or informational aspects of diagram use. The p...