Research abstracts

Non-verbal communication in classical logic

Ronald Fuller
Presented at the 2019 Winter Meeting of the Association for Symbolic Logic.

Uninterpreted logical structures are generally considered to have no meaning. But in disciplines of applied logic, such as information management and software engineering, uninterpreted structures are meaningful. Put another way, logical vocabularies and sentences can express meaning even when the value of object constants are unknown, incorrect or absent. Meaning can be conveyed by the mode of presentation alone. Frege called this sense, Carnap called it intension.

The Stanford Encyclopedia of Philosophy says outright "In classical first-order logic intension plays no role." This is misleading. It is true that no awareness of meaning is needed for a person or machine to analyze uninterpreted statements, or to create derived statements from them. And it is true that many such statements are indeed meaningless. Logicians use meaningless structures to teach and study logic. But when formed properly and meaning is intended they do convey meaning. When formed improperly and meaning is intended they convey an approximation or guess at the intended meaning, which can lead to problems.

Modern institutions rely heavily on disciplines of applied logic. For example, many institutions organize information into relational databases, which are based on logic. Leaders often want to combine or compare information between organizations but cannot because the metalanguage descriptions of similar relations are different, so some intended statements cannot be derived.

Logic literacy is necessary to convey any intended meaning using logic. The decline of logic education during the 20th century and the ensuing decline of logic literacy is the root cause of many difficult and costly challenges facing modern organizations.

First-order logic in 13th-century accounting systems

Ronald Fuller
Presented at the 2017 American Philosophical Association, Pacific Division conference, sessions for the Association for Symbolic Logic.

The system of interconnected books used in double-entry bookkeeping and other early accounting systems is precisely consistent with the relational model and, therefore, first-order logic. That means every object can be described in terms of the relational model and operated upon using a relational language. In other words, medieval merchants had created fully-functional, manually-operated relational database management systems, which exhibit quantification over relations with arities greater than one.

Primitive business institutions did not have the benefit of computers, but they enjoyed a particular advantage over their modern counterparts: a logic-literate merchant class. When the relational model was introduced in the 1970's it was falsely seen as a new computer-based method of organizing information, rather than a new computer-based way to automate old logic-based methods that had been used with success for nearly 700 years. Consequently, the responsibility to define logical vocabularies for information systems shifted to computer experts rather than business domain experts, leading to the widespread proliferation of defective ontologies that fail to meet organizational requirements. The de-emphasis of logic education since the 19th century is a significant factor in this predicament.

Logic Training and Its Role in Critical Thinking and Problem Solving

Ronald Fuller, Peter Cardon, Matt North
Presented at the 2018 conference of the International Association for Computer Information Systems

Study Background

Information systems and business school educators are constantly discussing how to improve critical thinking skills and problem-solving skills among their students. Furthermore, recruiters and alumni suggest critical thinking skills and problem-solving abilities are among the most important yet often lacking skill sets for graduates.

Our primary focus is on situations involving ambiguity and complexity. Information Systems and Business programs have traditionally been known for graduating highly analytical business professionals. However, many recent evaluations of such programs suggest that schools often fail to produce graduates who are effective and creative thinkers in highly unstructured situations (Datar, Garvin, & Cullen, 2010). Given the contemporary business environment—where exponentially growing amounts of unstructured information is readily available, where product cycles are shorter, where innovation is expected faster, and where technologies such as artificial intelligence are rapidly changing the nature of work—the ability to think critically is more important than ever. Furthermore, the ability to communicate precisely, concisely, and logically is a differentiating skill for many graduates.

Our central premise is that logic training leads to more effective critical thinking and problem solving. In fact, logic training is often the missing piece in significantly improving critical thinking and problem solving. While this may appear to be a somewhat simple idea, it is a largely contested notion (ASL Committee on Logic and Education, 1995; Attridge, Aberdein, & Inglis, 2016; Epp, 1997, 2001; Nisbet et al., 1987). Furthermore, even when this notion is accepted, it is rarely if ever applied to business education.

Study Methodology and Results

Our study focuses briefly on describing innovative approaches schools are taking to enhance the critical and creative thinking skills of their students. We also describe what we view as key considerations in how to develop curriculum, train instructors, and partner with industry to improve critical thinking.

Our research uses a case approach to explore the ways in which logic training, and the lack thereof, influence effective critical thinking and problem solving. The first case is based on developing queries in a database course. The case demonstrates how most students lack dynamic responsiveness to solving problems. In most cases, students can create a query that solves the problem in its static form. Yet, students rarely succeed in developing queries that will be successful when the underlying data or assumptions to the problem change. The second case focuses on pitch decks created in an entrepreneurship course and demonstrates the key logical flaws—in content and presentation—that students commonly make. Both cases are used to show how logic training can improve student performance.

Implications for Educators

Given the focus on critical thinking and problem solving by educators around the world, we believe it’s critical to identify the fundamental logic skills that support effective critical thinking and problem solving. Specifically, we have identified the following skills that teachers should emphasize:

  1. Recognize valid and invalid argument forms
  2. Distinguish between the form and content of an argument
  3. Understand the antecedents and consequents of their own assumptions or the claims of others
  4. Follow or construct a simple line of deductive reasoning
  5. Recognize ambiguity in their own communication and that of others
  6. Determine what conditions satisfy a simple set of rules or constraints

We demonstrate how educators can develop content and asses proficiency (i.e., rubrics) in these areas of logic training.


ASL Committee on Logic and Education. (1995). Guidelines for logic education. The Bulletin for Symbolic Logic, 1(1), 4-7.
Attridge, N., Aberdein, A., & Inglis, M. (2016). Does studying logic improve logical reasoning? In Csíkos, C., Rausch, A., & Szitányi, J. (Eds.). Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 27–34. Szeged, Hungary: PME.
Datar, S. M., Garvin, D. A., & Cullen, P. G. (2010). Rethinking the MBA: Business education at the crossroads. Boston: Harvard Business Review Press.
Epp, S. S. (1997). Logic and discrete mathematics in the schools. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 368, 75-83.
Epp, S. S. (2003). The role of logic in teaching proof. The American Mathematical Monthly, 110(1), 886-899.
Nisbett, R. E., Fong, G. T., Lehman, D. R., & Cheng, P W. (1987). Teaching reasoning. Science, 238, 625-631.


Ronald Fuller, Peter Cardon
Presented at the 2016 Joint Matheatics Meetings; published abstract.

Sophotaxis (Greek wisdom + order) combines the notion of entailment with that of intent. If a logical signature can be used to express an intended set of statements and their antecedents, then it is sophotaxically complete; if it cannot, then it is sophotaxically deranged or incomplete. This concept has important application in the field of enterprise information management. Organizations are frequently unable to produce desired outputs even when their systems are known to contain all necessary inputs. Important meaning and context is lost when those inputs are sophotaxically deranged. New information sources can be created by almost any individual at any level of an organization, so education in fundamental logic and logic-aware management are necessary if enterprise organizations wish to create information systems capable of meeting their expectations.


Logic is the missing link in information management

Ronald Fuller
Presented at the 2016 Joint Mathematics Meetings; published abstract.

People who manage information have known since the 1970s that logic can be used to query information in databases, but the use of logic to  organize information is not well understood by modern practitioners. Frike [1] states ”A greatly underappreciated and unused theoretical background to the organization of information is that of symbolic logic. (The monumental and authoritative Encyclopedia of Library and Information Sciences, Third Edition, 2009, does not have an entry for logic in its 6,856 pages ...)” (p 121). Yet effective methods of using logic to organize information were developed more than 700 years ago. This session will discuss the following: (a) how the system of interconnected books used in double-entry bookkeeping since the 13th century is precisely consistent with the relational model and, therefore, first-order logic; (b) how cultural and historical factors have undermined modern recognition of important principles and the effective use of logic in organizations; and (c) how logic education and practical application can help enterprise organizations overcome their most difficult and costly challenges in information management.

[1]  Martin Fricke,  Logic and the Organization of Information (Springer, 2012)