We describe Slate, a logic-based, robust interactive reasoning system that allows human “pilots” to harness an ensemble of intelligent agents in order to construct, test, and express various sorts of natural argumentation. Slate empowers students and professionals in the business of producing argumentation, e.g., mathematicians, logicians, intelligence analysts, designers and producers of stand...

1. Pohlers and The Problem. I first met Wolfram Pohlers at a workshop on proof theory organized by Walter Felscher that was held in Tübingen in early April, 1973. Among others at that workshop relevant to the work surveyed here were Kurt Schütte, Wolfram’s teacher in Munich, and Wolfram’s fellow student Wilfried Buchholz. This is not meant to slight in the least the many other fine logicians wh...

The paper investigates the strength of the anti-foundation axiom on the basis of various systems of constructive set theories. 1. Introduction Intrinsically circular phenomena have come to the attention of researchers in diiering elds such as mathematical logic, computer science , artiicial intelligence, linguistics, cognitive science, and philosophy. Logicians rst explored set theories whose u...

This article begins with an account of logic, and of how logicians formulate formal rules of inference for the sentential calculus, which hinges on analogs of negation and the connectives if, or, and and. It considers the various ways in which computer scientists have written programs to prove the validity of inferences in this and other domains. Finally, it outlines the principal psychological...

The present study intended to investigate the processing behavior of 2 groups of L2 learners of English (high and mid in proficiency) and a group of English native speakers on English active and passive reduced relative clauses. Three sets of tasks, an offline task, and 2 online tasks were conducted. Results revealed that the high-proficiency group’s performance was the same as that of the nati...

One of the surprising developments in the area of program verification is how ideas introduced by logicians in the early part of the 20th Century ended up yielding by the 21 Century industrial-standard property-specification languages. This development was enabled by the equally unlikely transformation of the mathematical machinery of automata on infinite words, introduced in the early 1960s fo...

We consider the problem of type checking for Java 5 with generics and wildcard types. Java supports type inference for methods with type parameters, but its presentation in the Java Language Specification lacks both clarity and a sense for how inference fits into the larger picture of Java’s type system. We show, in contrast, how this type inference can be cleanly integrated with subtyping of w...

In the psychological literature on reasoning it has always been assumed that if there is such a thing as mental logic, it must be a set of inference rules. This proof-theoretic conception of mental logic is compatible with but doesn’t do justice to what, according to most logicians, logic is about. Thus, the ongoing debate over mental logic is based on a too narrow notion of logic. Adopting the...

In epistemic logic, some axioms dealing with the notion of knowledge are rather convoluted and difficult to interpret intuitively, even though some of them, such as the axioms .2 and .3, are considered to be key axioms by some epistemic logicians. We show that they can be characterized in terms of understandable interaction axioms relating knowledge and belief or knowledge and conditional belie...