Towards Intuitive Reasoning in Axiomatic Geometry

Towards Complete Reasoning about Axiomatic Specifications

To support verification of expressive properties of functional programs, we consider algebraic style specifications that may relate multiple user-defined functions, and compare multiple invocations of a function for different arguments. We present decision procedures for reasoning about such universally quantified properties of functional programs, using local theory extension methodology. We e...

Notes on Axiomatic Geometry

Axiomatic Systems for Geometry∗

An axiomatic system contains a set of primitives and axioms. The primitives are Adaptation to the current course is in the margins. object names, but the objects they name are left undefined. This is why the primitives are also called undefined terms. The axioms are sentences that make assertions about the primitives. Such assertions are not provided with any justification, they are neither tru...

Unsolved Problems in Intuitive Geometry

Axiomatic Proofs through Automated Reasoning*

search of the seminal papers and significant books devoted to the study of various types of logic t e reveals that many proofs are missing. Indeed, if one seeks an axiomatic proof (of the type that Hilber njoyed) relying solely on, say, condensed detachment, in many cases one finds that none is offered by d t the literature. In part prompted by this discovery, we embarked on an intense study de...