Stuart Shapiro

AAAI Conference 2015 Conference Paper

Inference Graphs: Combining Natural Deduction and Subsumption Inference in a Concurrent Reasoner

• Daniel Schlegel
• Stuart Shapiro

There are very few reasoners which combine natural deduction and subsumption reasoning, and there are none which do so while supporting concurrency. Inference Graphs are a graph-based inference mechanism using an expressive first– order logic, capable of subsumption and natural deduction reasoning using concurrency. Evaluation of concurrency characteristics on a combination natural deduction and subsumption reasoning problem has shown linear speedup with the number of processors.

AAAI Conference 2014 Conference Paper

Inference Graphs: A New Kind of Hybrid Reasoning System

• Daniel Schlegel
• Stuart Shapiro

Hybrid reasoners combine multiple types of reasoning, usually subsumption and Prolog-style resolution. We outline a system which combines natural deduction and subsumption reasoning using Inference Graphs implementing a Logic of Arbitrary and Indefinite Objects.

AAAI Conference 2013 Conference Paper

Concurrent Reasoning with Inference Graphs

• Daniel Schlegel
• Stuart Shapiro

KR Conference 2010 Conference Paper

Set-Oriented Logical Connectives

• Stuart Shapiro

What is special about and and or is that they are associaOf the common commutative binary logical connectives, only and and or may be used as operators that take arbitrary numbers of arguments with order and multiplicity being irrelevant, that is, as connectives that take sets of arguments. This is especially evident in the Common Logic Interchange Format, in which it is easy for operators to be given arbitrary numbers of arguments. The reason is that and and or are associative and idempotent, as well as commutative. We extend the ability of taking sets of arguments to the other common commutative connectives by defining generalized versions of nand, nor, xor, and iff, as well as the additional, parameterized connectives andor and thresh. We prove that andor is expressively complete—all the other connectives may be considered abbreviations of it.

KR Conference 2004 Conference Paper

A Logic of Arbitrary and Indefinite Objects

• Stuart Shapiro

A Logic of Arbitrary and Indefinite Objects, LA, has been developed as the logic for knowledge representation and reasoning systems designed to support natural language understanding and generation, and commonsense reasoning. The motivations for the design of LA are given, along with an informal introduction to the theory of arbitrary and indefinite objects, and to LA itself. LA is then formally defined by presenting its syntax, proof theory, and semantics, which are given via a translation scheme between LA and the standard classical First-Order Predicate Logic. Soundness is proved. The completeness theorem for LA is stated, and its proof is sketched. LA is being implemented as the logic of SNePS3, the latest member of the SNePS family of Knowledge Representation and Reasoning systems.