17 research outputs found
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com
Realms: A Structure for Consolidating Knowledge about Mathematical Theories
Since there are different ways of axiomatizing and developing a mathematical
theory, knowledge about a such a theory may reside in many places and in many
forms within a library of formalized mathematics. We introduce the notion of a
realm as a structure for consolidating knowledge about a mathematical theory. A
realm contains several axiomatizations of a theory that are separately
developed. Views interconnect these developments and establish that the
axiomatizations are equivalent in the sense of being mutually interpretable. A
realm also contains an external interface that is convenient for users of the
library who want to apply the concepts and facts of the theory without delving
into the details of how the concepts and facts were developed. We illustrate
the utility of realms through a series of examples. We also give an outline of
the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201
A Foundational View on Integration Problems
The integration of reasoning and computation services across system and
language boundaries is a challenging problem of computer science. In this
paper, we use integration for the scenario where we have two systems that we
integrate by moving problems and solutions between them. While this scenario is
often approached from an engineering perspective, we take a foundational view.
Based on the generic declarative language MMT, we develop a theoretical
framework for system integration using theories and partial theory morphisms.
Because MMT permits representations of the meta-logical foundations themselves,
this includes integration across logics. We discuss safe and unsafe integration
schemes and devise a general form of safe integration
The Planetary System: Web 3.0 Active Documents for STEM
AbstractIn this paper we present the Active Documents Paradigm (semantically annotated documents associated with a content commons that holds the corresponding background ontologies) and the Planetary system (as an active document player). We show that the current Planetary system gives a solid foundation and can be extended modularly to address most of the criteria of the Executable Papers Challenge
Accessibility to possibilities : discover the unknown unknown worlds
The digital revolution has transformed the world, and today we are drowning in information. We use search engines as an efficient way to access information, and when we search, by connecting, relating, or random recommending, our knowledge network expands from the keyword we put in. With this search engine model, it’s easy for us to find what we know we don’t know. But it’s hard to access things we don’t know we don’t know. In other words, our past limits our accessibility to information.
In this essay, I attempt to find an alternative way of approaching information in the design process through constructing accessibility to all kinds of possibilities. I propose that we generate knowledge instead of search for it — design in a way where innovation and willingness are not trapped by the past, and allow more people to participate and have fun in the design process. Thus, we can integrate the design process into daily life and, ultimately, build a decentralized design ecosystem for society
Social Network Analysis: A Machine Learning Approach
Social Network Analysis (SNA) is an appealing research topic, within the domain of Artificial Intelligence (AI), owing to its widespread application in the real world. In this dissertation, we have proposed effective Machine Learning (ML) and Deep Learning (DL) approaches toward resolving these open problems with regard to SNA, viz: Breakup Prediction, Link Prediction, Node Classification, Event-based Analysis, and Trend/Pattern Analysis. SNA can be employed toward resolving several real-world problems; and ML as well as DL have proven to be very effective methodologies for accomplishing Artificial Intelligence (AI)- related goals. Existing literature have focused on studying the apparent and latent interactions within social graphs as an n-ary operation, which yields binary outputs comprising positives (friends, likes, etc.) and negatives (foes, dislikes, etc.). Inasmuch as interactions constitute the bedrock of any given Social Network (SN) structure; there exist scenarios where an interaction, which was once considered a positive, transmutes into a negative as a result of one or more indicators which have affected the interaction quality. At present, this transmutation has to be manually executed by the affected actors in the SN. These manual transmutations can be quite inefficient, ineffective, and a mishap might have been incurred by the constituent actors and the SN structure prior to a resolution. Thus, as part of the research contributions of this dissertation, we have proposed an automatic technique toward flagging positive ties that should be considered for breakups or rifts (negative-tie state), as they tend to pose potential threats to actors and the SN. Furthermore, in this dissertation, we have proposed DL-based approaches based on edge sampling strategy for resolving the problems of Breakup Prediction, Link Prediction, and Node Classification. Also, we have proposed ML-based approaches for resolving the problems of Event-based Analysis and Trend/Pattern Analysis. We have evaluated our respective approaches against benchmark social graphs, and our results have been comparatively encouraging as documented herein
Early Christianity and Ancient Astrology
Early Christianity and Ancient Astrology explores a variety of responses to astrology, the most popular form of divination among early Christians in Greco-Roman antiquity. After a brief overview of ancient astrological theory and a survey of polemical responses to it, this book documents instances in which early Christian writers and communities incorporated astrology positively into their beliefs and practices. This study is of interest to students of early Christianity and of Greco-Roman religion and to those concerned with interfaith relations or with issues of Christian unity and diversity. It is particularly recommended for use in courses on the history of Christianity and on the religions of Greco-Roman antiquity