Logical Reasoning with Diagrams and Sentences: Using Hyperproof (Lecture Notes)

The Logical Reasoning with Diagrams and Sentences courseware package teaches the principles of analytical reasoning and proof construction using a carefully crafted combination of textbook, desktop, and online materials. This package is sure to be an essential resource in a range of courses incorporating logical reasoning, including formal linguistics, philosophy, mathematics, and computer science.

Unlike traditional formal treatments of reasoning, this package uses both graphical and sentential representations to reflect common situations in everyday reasoning where information is expressed in many forms, such as finding your way to a location using a map and an address. It also teaches students how to construct and check the logical validity of a variety of proofs—of consequence and non-consequence, consistency and inconsistency, and independence—using an intuitive proof system which extends standard proof treatments with sentential, graphical, and heterogeneous inference rules, allowing students to focus on proof content rather than syntactic structure. Building upon the widely used Tarski’s World and Language, Proof and Logic courseware packages, Logical Reasoning with Diagrams and Sentences contains more than three hundred exercises, most of which can be assessed by the Grade Grinder online assessment service; is supported by an extensive website through which students and instructors can access online video lectures by the authors; and allows instructors to create their own exercises and assess their students’ work.

Logical Reasoning with Diagrams and Sentences is an expanded revision of the Hyperproof courseware package.

Dave Barker-Plummer is a senior research scientist with the Openproof Project at the Center for the Study of Language and Information (CSLI). Jon Barwise (1942–2000) was professor of philosophy, mathematics, and computer science at Indiana University and one of the founding members of CSLI. John Etchemendy is professor of philosophy and symbolic systems at Stanford University and a former director of CSLI.