The Role of Logic and Ontology in Language and Reasoning

Natural languages have words for all the operators of first-order logic, modal logic, and many logics that have yet to be invented. They also have words and phrases for everything that anyone has ever discovered, assumed, or imagined. Aristotle invented formal logic as a tool (organon) for analyzing and reasoning about the ontologies implicit in language. Yet some linguists and logicians took a major leap beyond Aristotle: they claimed that there exists a special kind of logic at the foundation of all NLs, and the discovery of that logic would be the key to harnessing their power and implementing them in computer systems. Projects in artificial intelligence developed large systems based on complex versions of logic, yet those systems are fragile and limited in comparison to the robust and immensely expressive natural languages. Formal logics are too inflexible to be the foundation for language; instead, logic and ontology are abstractions from language. This reversal turns many theories about language upside down, and it has profound implications for the design of automated systems for reasoning and language understanding. This article analyzes these issues in terms of Peirce’s semiotics and Wittgenstein’s language games. The resulting analysis leads to a more dynamic, flexible, and extensible basis for ontology and its use in formal and informal reasoning. This article is a slightly revised preprint of Chapter 11 in Theory and Applications of Ontology: Philosophical Perspectives, edited by R. Poli & J. Seibt, Berlin: Springer, pp. 231-263. 1. The Search for Foundations Natural languages are the most sophisticated systems of communication ever developed. Formal ontologies are valuable for applications in science, engineering, and business, but they have been difficult to generalize beyond narrowly defined microtheories for specialized domains. For language understanding, formal systems have only been successful in narrow domains, such as weather reports and airline reservations. Frege, Russell, and the Vienna Circle tried to make formal logic the universal language of science, but that attempt failed. Only the final results of any research can be stated formally, never the vague hunches, intuitive explorations, and heated debates that are necessary for any creative advance. Scientists and engineers criticized formal methods with the pithy slogans “Physicists don’t do axioms” and “All models are wrong, but some are useful.” Even Aristotle, who invented the first formal logic, admitted that his syllogisms and categories are important for stating the results of research, but that informal methods are necessary for gathering and interpreting empirical evidence. Aristotle’s logic and categories still serve as a paradigm for the ontologies used in modern computer systems, but his grand synthesis began to break down in the 16th century. Aristotle’s physics and cosmology were demolished by the work of Copernicus, Galileo, Kepler, and Newton. In philosophy, the skeptical tradition of antiquity was revived by the publication in 1562 of a new edition of the works of Sextus Empiricus, whose attacks on Aristotle were popularized by the essays of Michel de Montaigne. In responding to the skeptics, Descartes began his search for certainty from the standpoint of universal doubt, but he merely reinforced the corrosive effects of skepticism. The British empiricists responded with new approaches to epistemology, which culminated in Hume’s devastating criticisms of the foundations of science itself. Two responses to Hume helped to restore the legitimacy of science: Thomas Reid’s critical common sense and Immanuel Kant’s three major Critiques. Kant (1787) adopted Aristotle’s logic as the basis for his new system of categories, which he claimed would be sufficient for defining all other concepts: If one has the original and primitive concepts, it is easy to add the derivative and subsidiary, and thus give a complete picture of the family tree of the pure understanding. Since at present, I am concerned not with the completeness of the system, but only with the principles to be followed, I leave this supplementary work for another occasion. It can easily be carried out with the aid of the ontological manuals. (A:82, B:108) Two centuries later, Kant’s “easy” task is still unfinished. His Opus postumum records the struggles of the last decade of his life when Kant tried to make a transition from his a priori metaphysics to the experimental evidence of physics. Förster (2000) wrote “although Kant began this manuscript in order to solve a comparatively minor problem within his philosophy, his reflections soon forced him to readdress virtually all the key problems of his critical philosophy: the objective validity of the categories, the dynamical theory of matter, the nature of space and time, the refutation of idealism, the theory of the self and its agency, the question of living organisms, the doctrine of practical postulates and the idea of God, the unity of theoretical and practical reason, and, finally, the idea of transcendental philosophy itself.” Unlike Aristotle, who used logic as a tool for analyzing language, Kant assumed that logic is a prerequisite, not only for language, but for all rational thought. Richard Montague (1970) pushed Kant’s assumption to an extreme: “I reject the contention that an important theoretical difference exists between formal and natural languages.” That assumption, acknowledged or not, motivated much of the research in artificial intelligence and formal linguistics. The resulting systems are theoretically impressive, but they cannot learn and use ordinary language with the ease and flexibility of a threeyear-old child. But if logic is inadequate, what other foundation could support linguistics and AI? What kind of semantics could represent the highly technical formalisms of science, the colloquial speech of everyday life, and the requirements for sharing and reasoning with the knowledge scattered among millions of computers across the Internet? How would the research and development change under the assumption that logic is a derivative from language, not a prerequisite for it? One major change would be a shift in emphasis from the rigid views of Frege, Russell, and Carnap to the more flexible philosophies of Peirce, Whitehead, and the later Wittgenstein. As logicians, those two groups were equally competent, but the former considered logic to be superior to language, while the latter recognized the limitations of logic and the power of language. Peirce, in particular, was a pioneer in logic, but he included logic within the broader field of semiotics, or as he spelled it, semeiotic. That broader view relates the precise formalisms of grammar and logic to the more primitive, yet more flexible mechanisms of perception, action, and learning. Language is based on vocal signs and patterns of signs, whose more stable forms are classified as vocabulary and grammar. But instead of starting with formal precision, the first signs are vague, ambiguous, and uncertain. Precision is a rare state that never occurs in the early stages of learning, and absolute precision is unattainable in any semiotic system that represents the real world. Grammar, logic, and ontology describe stable patterns of signs or invariants under transformations of perspective. Those stable patterns, which are fossilized in formal theories, develop as each individual interacts with the world and other creatures in it. Although formal logic can be studied independently of natural language semantics, no formal ontology that has any practical application can ever be developed and used without acknowledging its intimate connection with NL semantics. An ontology for medical informatics, for example, must be related to medical publications, to a physician’s diagnoses, and to the discussions among general practitioners, specialists, nurses, patients, and the programmers who develop the software they use. All these people are constantly thinking and using NL semantics, not the formal axioms of some theory. Frege (1879) hoped “to break the domination of the word over the human spirit by laying bare the misconceptions that through the use of language often almost unavoidably arise concerning the relations between concepts.” Wittgenstein agreed that language can be misleading, but he denied that an artificial language could be better. At best, it would be a different language game (Sprachspiel). These philosophical observations explain why large knowledge bases such as Cyc (Lenat 1995) have failed to achieve true artificial intelligence. An inference engine attached to a large collection of formally defined facts and axioms can prove theorems more efficiently than most people, but it lacks the flexibility of a child in learning new information and adapting old information to new situations (Sowa 2005). Two computer scientists who devoted their careers to different aspects of AI have concluded that the goal of a fixed formal ontology of everything is both unattainable and misguided. Alan Bundy, who developed formal methods for theorem proving and problem solving, proposed ontology evolution as a method for systematically relating smaller domain ontologies and adapting them to specific problems (Bundy & McNeill 2006; Bundy 2007). Yorick Wilks, who developed informal methods of preference semantics for natural language processing, maintained that the lexical resources used in language analysis and interpretation are sharply distinct from and should not be confused with formal ontologies (Wilks 2006, 2008a,b). These two views can be reconciled by using linguistic information as the basis for indexing and relating an open-ended variety of task-oriented ontologies. Instead of a static ontology, this article develops a dynamic approach that can relate the often vague and shifting meanings of ordinary words to the formal ontologies needed for computer appli