A Corpus of Spatial Reasoning Problems

Spatial reasoning is an important part of common-sense reasoning but has most often been examined in isolation from other areas of common sense knowledge representation. Spatial reasoning also has been a prominent area of research in linguistic semantics. In this work, we aim to create a corpus of common sense reasoning problems formalized in the context of a large and comprehensive theory of world knowledge, in the hopes that it will be more generally reusable on a wide variety of practical reasoning problems. An additional goal is to demonstrate the computational sufficiency of this work by employing automated reasoning to solve the problems. Finally, we also state the problems first in natural language, to provide a set of test cases for theories of linguistic semantics and computational linguistics, with a computational representation that can help to validate whether any method or process of interpreting language into a computational logic representation is correct or sufficient. This is an ambitious set of goals, and it will not be possible to provide solutions for all the problems that could be formulated in natural language. In particular, we do not attempt to create an implementation, at least at this time, for a system that can translate all of the stated problems from language to logic. Many of the problems also appear to require a logic and reasoning system beyond first order logic. It is important however, to have challenges that are unsolved in order to motivate research.