•  124
    Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural langu…Read more
  •  98
    On an unsound proof of the existence of possible worlds
    Notre Dame Journal of Formal Logic 30 (4): 598-603. 1989.
    In this paper, an argument of Alvin Plantinga's for the existence of abstract possible worlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.
  •  81
    Reference ontologies — application ontologies: Either/or or both/and?
    In Pierre Grenon, Christopher Menzel & Barry Smith (eds.), Proceedings of the KI 2003 Workshop on Reference Ontologies and Application Ontologies, Ceur Workshop Proceedings, Vol. 94. 2004.
    The distinction between reference ontologies and application ontologies crept rather unobtrusively into the recent literature on knowledge engineering. A lot of the discourse surrounding this distinction – notably, the one framing the workshop generating this collection of papers – suggests the two types of ontologies are in some sort of opposition to one another. Thus, Borge et al. [3] characterize reference ontologies (more recently, foundational ontologies) as rich, axiomatic theories whose f…Read more
  •  76
    Logic and Reality: Essays on the Legacy of Arthur Prior
    Philosophical Review 109 (2): 281. 2000.
    Arthur Prior was a truly philosophical logician. Though he believed formal logic to be worthy of study in its own right, of course, the source of Prior’s great passion for logic was his faith in its capacity for clarifying philosophical issues, untangling philosophical puzzles, and solving philosophical problems. Despite the fact that he has received far less attention than he deserves, Prior has had a profound influence on the development of philosophical and formal logic over the past forty ye…Read more
  •  66
    The Process Specification Language: Theory and Applications
    with Michael Grüninger
    AI Magazine 24 (3): 63-74. 2003.
    The Process Specification Language (PSL) has been designed to facilitate correct and complete exchange of process information among manufacturing systems, such as scheduling, process modeling, process planning, production planning, simulation, project management, work flow, and business process reengineering. We given an overview of the theories with the PSL ontology, discuss some of the design principles for the ontology, and finish with examples of process specifications that are based on the …Read more
  •  65
    Frege Numbers and the Relativity Argument
    Canadian Journal of Philosophy 18 (1): 87-98. 1988.
    Textual and historical subtleties aside, let's call the idea that numbers are properties of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed some light on…Read more
  •  65
    Ontology theory
    In Jerome Euzenat, Asuncion Gomez-Perez, Nicola Guarino & Heiner Stuckenschmidt (eds.), CEUR Workshop Proceedings, Vol. 64, . 2002.
    Ontology today is in many ways in a state similar to that of analysis in the late 18th century prior to arithmetization: it lacks the sort rigorous theoretical foundations needed to elevate ontology to the level of a genuine scientific discipline. This paper attempts to make some first steps toward the development of such foundations. Specifically, starting with some basic intuitions about ontologies and their content, I develop an expressively rich framework capable of treating ontologies as th…Read more
  •  56
    SCL: A Logic Standard for Semantic Integration
    with Patrick Hayes
    Semantic Integration, CEUR Workshop Proceedings, Vol. 82 (2003). 2003.
    The Knowledge Interchange Format (KIF) [2] is an ASCII- based framework for use in exchanging of declarative knowledge among disparate computer systems. KIF has been widely used in the fields of knowledge engineering and artificial intelligence. Due to its growing importance, there arose a renewed push to make KIF an offi- cial international standard. A central motivation behind KIF standardization is the wide variation in quality, style, and content — of logic-based frameworks being used for knowl…Read more
  •  46
    In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic
  •  46
    A Formal Foundation for Process Modeling
    with Michael Grüninger
    In C. Welty B. Smith (ed.), Formal Ontology in Information Systems (FOIS), Acm Press. 2001.
    Process modeling is ubiquitous in business and industry. While a great deal of effort has been devoted to the formal and philosophical investigation of processes, surprisingly little research connects this work to real world process modeling. The purpose of this paper is to begin making such a connection. To do so, we first develop a simple mathematical model of activities and their instances based upon the model theory for the NIST Process Specification Language (PSL), a simple language for descr…Read more
  •  28
    Structuralism and Conceptual Change in Mathematics
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990. 1990.
    I address Grosholz's critique of Resnik's mathematical structuralism and suggest that although Resnik's structuralism is not without its difficulties it survives Grosholz's attacks.
  •  15
    Proceedings of the KI 2003 Workshop on Reference Ontologies and Application Ontologies (edited book)
    with Pierre Grenon and Barry Smith
    CEUR Workshop Proceedings, Vol. 94. 2004.
    Contains the following contributions: Ingvar Johansson: Ontologies and Concepts. Two Proposals Christopher Menzel: Reference Ontologies - Application Ontologies: Either/Or or Both/And? Luc Schneider: Foundational Ontologies and the Realist Bias Guenther Goerz, Kerstin Buecher, Bernd Ludwig, Frank-Peter Schweinberger, and Iman Thabet: Combining a Lexical Taxonomy with Domain Ontology in the Erlangen Dialogue System Vim Vandenberghe, Burkhard Schafer, John Kingston: Ontology Modelling in the Lega…Read more
  •  9
    Meaning and Argument (review)
    Philosophical Books 44 (1): 69-70. 2003.
    A review of the 1st edition of Lepore's Meaning and Argument, in which the reviewer (me), on the one hand, says that the text contains no proof theory and, on the other, subsequently notes that Lepore makes use of the truth tree method. I guess, at the time, I thought that only axiomatic systems and natural deduction systems fell under the rubric "proof theory". Sorry. Other than that I suppose the review is mildly informative.
  •  4
    Providing a means of translating RDF, RDF-S, and DAML+OIL descriptions into a first-order predicate calculus logical theory not only specifies the intended meaning of the descriptions, but also produces a representation of the descriptions from which inferences can automatically be made using traditional automatic theorem provers and problem solvers. For example, the DAML+OIL axioms enable a reasoner to infer from the two statements “Class Male and class Female are disjointWith.” and “John is ty…Read more
  •  4
    Structuralism and Conceptual Change in Mathematics
    PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990 (2): 397-401. 1990.
    Professor Grosholz packs a lot into her interesting and suggestive paper “Formal Unities and Real Individuals” (Grosholz 1990b). In the limited space available I can comment briefly on its several parts, or direct more substantive comments at a single issue. I will opt for the latter; specifically, I want to address her critique of mathematical structuralism, as found especially in the writings of Michael Resnik.I begin with a brief, hence necessarily caricatured, summary of Resnik’s influential…Read more
  • Mathematical Realism and the Theory of Sets
    Dissertation, University of Notre Dame. 1984.
    Set theoretic platonism is the view that there exist objective, mind-independent abstract sets, and that set theory is the science of these entities. For the realist, this view offers the most natural semantical account of set theoretic discourse. Nonetheless, set theoretic platonism is beset by a number of serious difficulties. Chief among these, it turns out, is that it must deny the fundamental set theoretic intuition that any available objects can be collected into a further object. After a …Read more
  • The argument from collections
    In Jerry L. Walls & Trent Dougherty (eds.), Two Dozen (or so) Arguments for God: The Plantinga Project, Oxford University Press. 2018.
  • Actualism
    In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.