Angwin, CA, United States
Angwin, CA, United States

Time filter

Source Type

Pease A.,Articulate Software | Sutcliffe G.,University of Miami | Siegel N.,Articulate Software | Trac S.,University of Miami
AI Communications | Year: 2010

The Suggested Upper Merged Ontology (SUMO) has provided the TPTP problem library with problems that have large numbers of axioms, of which typically only a few are needed to prove any given conjecture. The LTB division of the CADE ATP System Competition tests the performance of ATP systems on these types of problems. The SUMO problems were used in the SMO category of the LTB division in 2008. This paper presents an analysis of the performance of the 2007 and 2008 CASC entrants on the SUMO problems, illustrating the improvements that can be achieved by various tuning techniques. © 2010 - IOS Press and the authors. All rights reserved.

Reed S.K.,San Diego State University | Reed S.K.,Stanford University | Pease A.,Articulate Software
Cognitive Systems Research | Year: 2015

Psychoinformatics is an emerging discipline that uses tools from the information sciences to organize psychological data. This article supports that objective by proposing a framework for constructing cognition ontologies by using WordNet, FrameNet, and the Suggested Upper Merged Ontology (SUMO). The first section describes the major characteristics of each of these tools. WordNet is a large lexical data base that was begun in the 1980s by George Miller. FrameNet is a database of event schemas based on a theory of frame semantics developed by the linguist Charles Fillmore. SUMO is a formal ontology of concepts expressed in mathematical logic that supports deductive reasoning. The next section discusses the objectives of science ontologies and includes examples for psychoses and for emotion. The article then describes potential applications of cognition ontologies for (1) studying how people organize knowledge, (2) analyzing major theoretical concepts such as abstraction, and (3) formulating premises that can serve as a link between informal taxonomies and formal ontologies. The final section discusses extending cognition ontologies to related domains such as artificial intelligence and cognitive neuroscience. © 2014 Elsevier B.V.

Benzmuller C.,Articulate Software
Annals of Mathematics and Artificial Intelligence | Year: 2011

Numerous classical and non-classical logics can be elegantly embedded in Church's simple type theory, also known as classical higher-order logic. Examples include propositional and quantified multimodal logics, intuitionistic logics, logics for security, and logics for spatial reasoning. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Off-the-shelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about embedded logics and logics combinations. In this article we focus on combinations of (quantified) epistemic and doxastic logics and study their application for modeling and automating the reasoning of rational agents. We present illustrating example problems and report on experiments with off-the-shelf higher-order automated theorem provers. © 2011 Springer Science+Business Media B.V.

Pease A.,Articulate Software | Schulz S.,TU Munich
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

The Suggested Upper Merged Ontology (SUMO) is a large, comprehensive ontology stated in higher-order logic. It has co-evolved with a development environment called the Sigma Knowledge Engineering Environment (SigmaKEE). A large and important subset of SUMO can be expressed in first-order logic with equality. SigmaKEE has integrated different reasoning systems in the past, but they either had to be significantly modified, or integrated in a way that multiple queries to the same theory required expensive full re-processing of the full knowledge base. To overcome this problem, to create a simpler system configuration that is easier for users to install and manage, and to integrate a state-of-the-art theorem prover we have now integrated Sigma with the E theorem prover. The E distribution includes a simple server version that loads and indexes the full knowledge base, and supports interactive queries via a simple interface based on text streams. No special modifications to E were necessary for the integration, so SigmaKEE can be easily upgraded to future versions. © 2014 Springer International Publishing Switzerland.

Benzmuller C.,Free University of Berlin | Pease A.,Articulate Software
Journal of Web Semantics | Year: 2012

This article addresses the automation of higher-order aspects in expressive ontologies such as the suggested upper merged ontology SUMO. Evidence is provided that modern higher-order automated theorem provers like LEO-II can be fruitfully employed for the task. A particular focus is on embedded formulas (formulas as terms), which are used in SUMO, for example, for modeling temporal, epistemic, or doxastic contexts. This modeling is partly in conflict with SUMO's assumption of a bivalent, classical semantics and it may hence lead to counterintuitive reasoning results with automated theorem provers in practice. A solution is proposed that maps SUMO to quantified multimodal logic which is in turn modeled as a fragment of classical higher-order logic. This way automated higher-order theorem provers can be safely applied for reasoning about modal contexts in SUMO. Our findings are of wider relevance as they analogously apply to other expressive ontologies and knowledge representation formalisms. © 2011 Elsevier B.V. All rights reserved.

Pease A.,Articulate Software | Benzmuller C.,Free University of Berlin
AI Communications | Year: 2013

Sigma is an open source environment for the development of logical theories. It has been under development and regular release for nearly a decade, and has been the principal environment under which the open source Suggested Upper Merged Ontology (SUMO) has been created. We discuss its features and evolution, and explain why it is an appropriate environment for the development of expressive ontologies in first and higher order logic. © 2013 - IOS Press and the authors. All rights reserved.

Benzmuller C.,Articulate Software
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be elegantly embedded in simple type theory. Furthermore, simple type theory is sufficiently expressive to model combinations of embedded logics and it has a well understood semantics. Off-the-shelf reasoning systems for simple type theory exist that can be uniformly employed for reasoning within and about combinations of logics. Combinations of modal logics and other logics are particularly relevant for multi-agent systems. © 2010 Springer-Verlag Berlin Heidelberg.

Agency: GTR | Branch: EPSRC | Program: | Phase: Research Grant | Award Amount: 389.56K | Year: 2012

This research applies methods and tools from mathematical knowledge management and theorem proving to theoretical economics, by working with a class of cooperative games called pillage games. Pillage games, introduced by Jordan in 2006, provide a formal way of thinking about the ability of powerful coalitions to take resources from less powerful ones. While their name suggests primitive, violent interactions, pillage games are more applicable to advanced democracies, in which coalitions seek to form governments to alter the distribution of societys resources in their favour. If, for some allocation of societys resources, the coalition preferring another allocation is stronger than that preferring the status quo, the other allocation `dominates the status quo. The most conceptually intriguing, and the most computationally intractable solution concept for cooperative games is the `stable set. A stable set, has two features: no allocation in the set dominates another; each allocation outside the set is dominated by an allocation in the set. For pillage games with three agents under a few additional conditions, we have determined when stable sets exist, that they are unique and contain no more than 15 allocations, and how to determine them for a given power function. In this research, we first formally represent the mathematical knowledge developed in Jordans and our work using sTeX, a mathematical knowledge management tool. This allows, e.g., automatic identification of how various results depend on each other. We then use two modern automated theorem provers (ATPs), Isabelle and Theorema, to formally prove these results. Theorem proving is a hard task and if not provided with domain specific knowledge ATPs have to search through big search spaces in order to find proofs. To increase their reasoning power, we shall seek to identify recurring patterns in proofs, and extract proof tactics, reducing the interactions necessary to prove the theorems interactively. As important results in pillage games can be summarised in pseudo-algorithms, containing both computational and non-computational steps, we shall study such pseudo-algorithms, seeking to push them towards the much more efficient computational steps. Finally, we shall use the identified proof tactics to help the ATPs prove new results in order evaluate their true value. The research seeks to make a number of contributions. For theorem proving, pillage games form a new set of challenge problems. As the study of pillage games is new, and the canon of applicable knowledge small, this gives an unprecedented opportunity to encode most of it. The research will expand the tractable problem domain for ATPs; and - by identifying successful tactics - increase both the efficiency with which ATPs search for proofs, and - ideally - their ability to establish new results. For economics, this is the first major application of formal knowledge management and theorem proving techniques. The few previous applications of ATP to economics have formalised isolated results without engaging economists and have thus largely gone unnoticed by the discipline. As cooperative games are a known hard class of economic problems, and pillage games known to be tractable, this research therefore presents a strong `proof of concept for the use of ATP within economics. Cooperative game theory is formally similar to graph theory, the techniques and insights developed may be applicable to matching problems, network economics, operations research, and combinatorial optimisation more generally. Additionally, the researchers will introduce ATP techniques to the leading PhD summer school in computational economics, and are working in collaboration with economic theorists with strong computational backgrounds. Thus, the research seeks to form a focal point for formal knowledge management and theorem proving efforts in economics.

Loading Articulate Software collaborators
Loading Articulate Software collaborators