Language and Logic

With M. Böttner and L. Liang. (1998) Machine Learning of Physics Word Problems: A Preliminary Report. In A. Aliseda and R. van Glabbeeck, (Eds.), Computing Natural Language, Stanford, CA: CSLI Publications, 141-154.

With M. Böttner. (1998) Robotic Machine Learning of Anaphora. In Robotica, 16, 425-431.

With R. Sommer. (1997) Dispensing with the continuum. Journal of Mathematical Psychology, 41, 3-10.

With L. Liang. (1996) Probabilistic association and denotation in machine learning of natural language. In A. Gammerman (Ed.), Computational Learning and Probabilistic Reasoning. Sussex, England: John Wiley & Sons, Ltd., 87 Ð 100.

With S. Takahashi. (1996) Hierarchical learning of Boolean functions. In P.I. Bystrov and V.N. Sadovsky (Eds.), Philosophical Logic and Logical Philosophy, Essays in Honor of Vladimir A. Smirnov. Dordrecht, Netherlands: Kluwer Academic Publishers, 51 Ð 61.


With M. Böttner and L. Liang. (1996) Machine learning comprehension grammars for ten languages. Computational Linguistics 22, 329-350.

With R. Sommer. (1996) Finite models of elementary recursive nonstandard analysis. Notas de la Sociedad Matematica de Chile, 15, 73-95.

(1996) Forward. In Philip J. Ivanhoe (Ed.), Chinese Language, Thought, and Culture: Nivison and his Critics. Chicago: Open Court, 1996, vii-x.

With R. Chuaqui. (1995) Free-variable axiomatic foundations of infinitesimal analysis: A fragment with finitary consistency proof. Journal of Symbolic Logic, 60, 122-159.

With M. Böttner, L. Liang, and R. Ravaglia. (1995) Machine learning of natural language: problems and prospects. In M. de Glas & Z. Pawlak (Eds.), Proceedings of the Second Conference on the Fundamentals of Artificial Intelligence, Angkor, 511-525.


With M. Böttner & L. Liang. (1995) Comprehension grammars generated from machine learning of natural language. Machine Learning, 19, 133-152.

(1994) Some questions about Adams' conditionals. In E. Eells & B. Skyrms (Eds.), Probability and Conditionals: Belief Revision and Rational Decision. Cambridge: Cambridge University Press, 5-11.

(1994) A brief survey of Adams' contributions to philosophy. In E. Eells & B. Skyrms (Eds.), Probability and Conditionals: Belief Revision and Rational Decision. Cambridge: Cambridge University Press, 201-204.

With C. Crangle. (1994) Language and Learning for Robots. Stanford, CA: CSLI Publications, 276 pp.

With R. Chuaqui. (1993) A finitarily consistent free-variable positive fragment of infinitesimal analysis. Proceedings of the IX Latin American Symposium on Mathematical Logic, held at Bahia Blanca, Argentina, August 1992. Notas de Logica Matematica, 38, 1-59

With C. Crangle. (1993) An Analysis of `If' Sentences from the Standpoint of Communication. Journal of Literary Semantics 22, 1-23.

With M. Böttner & L. Liang. (1992) Comprehension grammars generated from machine learning of natural language. Preliminary version. In P. Dekker & M. Stokhof (Eds.), Proceedings of the Eighth Amsterdam Colloquium, Institute for Logic, Language and Computation, University of Amsterdam, 93-112.


With L. Liang & M. Böttner. (1992) Complexity issues in robotic machine learning of natural language. In L. Lam & V. Naroditsky (Eds.), Modelling Complex Phenomena. New York: Springer Verlag, 102-127.

(1991) Definition II: Rules of definition. In H. Burkhardt & B. Smith (Eds.), Handbook of Metaphysics and Ontology, Vol. 1: A-K. Munich; Philadelphia; Vienna: Philosophia (Analytica), 204-208.

(1991) Language for Humans and Robots. Oxford, England: Blackwell, 417 pp.

With R. Chuaqui. (1990) An equational deductive system for the differential and integral calculus. In P. Martin-Lof and G. Mints (Eds.) Lecture Notes in Computer Science, Proceedings of COLOG-88 International Conference on Computer Logic, held in Tallinn, USSR. Berlin Heidelberg: Springer Verlag, 25-49.

(1989) Commemorative Meeting for Alfred Tarski, Stanford University, November 7, 1983. In Peter Duren (Ed.), A Century of Mathematics in America, Part III. Providence, RI: American Mathematical Society, 395-396.

With C. Crangle. (1989) Geometrical semantics for spatial prepositions. In P.A. French, T.E. Uehling, Jr., and H. K. Wettstein (Eds.) Midwest Studies in Philosophy, XIV. Notre Dame, IN: University of Notre Dame Press, 399-422.

With S. Takahashi. (1989) An interactive calculus theorem-prover for continuity properties. Journal of Symbolic Computation, 7, 573-590.

With C. Crangle. (1988) Context-fixing semantics for the language of action. In J. Dancy, J.M.E. Moravcsik, & C.C.W. Taylor (Eds.), Human Agency: Language, duty, and value. Stanford, CA: Stanford University Press, 47-76, 288-290.

(1988) Philosophical implications of Tarski's work. Journal of Symbolic Logic, 53, 80-91.

(1985) Congruency theory of propositions. In Mérites et limites des Méthodes Logiques en Philosophie, Colloque international organisépar la Fondation Singer-Polignac en juin 1984. Paris: Librairie Philosophique J. Vrin, 279-299.

(1985) The primacy of utterer's meaning. In R. E. Grandy and R. Warner (Eds.), Philosophical Grounds of Rationality: Intentions, Categories, Ends. Oxford: Clarendon Press, 109-129.

With J. McDonald. (1984) Student use of an interactive theorem prover. In W. W. Bledsoe and D. W. Loveland (Eds.), Automated Theorem Proving: After 25 years. Providence, RI: American Mathematical Society. Contemporary Mathematics, 1984, 29, 315-360.

(1984) The next generation of interactive theorem provers. In R. E. Shostak (Ed.), Proceedings of the 7th International Conference on Automated Deduction, Napa, California, May 14-16, 1984, Lecture Notes in Computer Science #170. New York: Springer-Verlag, 303-315.

(1984) A puzzle about responses and congruence of meaning. Synthese, 58, 39-50.

(1983) Language learning in the limit. (Review/K. Wexler & P. W. Culicover: Formal Principles of Language Acquisition.) Contemporary Psychology, 28, 5-6.

(1982) Variable-free semantics with remarks on procedural extensions. In T. W. Simon & R. J. Scholes (Eds.), Language, Mind, and Brain. Hillsdale, NJ: Erlbaum, 21-34.

With J. Sheehan. (1981) CAI course in logic. In P. Suppes (Ed.), University-level Computer-assisted Instruction at Stanford: 1968-1980. Stanford, CA: Stanford University, Institute for Mathematical Studies in the Social Sciences, 193-226.

With J. Sheehan. (1981) CAI course in axiomatic set theory. In P. Suppes (Ed.), University-level Computer-assisted Instruction at Stanford: 1968-1980. Stanford, CA: Stanford University, Institute for Mathematical Studies in the Social Sciences, 3-80.

(1981) Direct inference in English. Teaching Philosophy, 4, 405-418.

(1980) In J. Speck (Ed.), Handbuch wissenschaftstheoretischer Begriffe. Göttingen, Germany: Vandenhock & Ruprecht: "Definition," Vol. 1, 124-129; "Grösse," Vol. 2, 268-269; "Mengenlehre," Vol. 2, 411-415; "Messung," Vol. 2, 415-423; "Observable," Vol. 2, p. 464.

(1980) Procedural semantics. In R. Haller & W. Grassl (Eds.), Language, Logic, and Philosophy, Proceedings of the 4th International Wittgenstein Symposium, Kirchberg am Wechsel, Austria 1979. Vienna: Hölder-Pichler-Tempsky, 27-35.

(1979) Logical inference in English: A preliminary analysis. Studia Logica, 38, 375-391.

(1979) Variable-free semantics for negations with prosodic variation. In E. Saarinen, R. Hilpinen, I. Niiniluoto, & M. P. Hintikka (Eds.), Essays in Honour of Jaakko Hintikka. Dordrecht: Reidel, 49-59.

With E. Macken. (1978) Steps toward a variable-free semantics of attributive adjectives, possessives, and intensifying adverbs. In K. E. Nelson (Ed.), Children's Language, Vol. 1. New York: Gardner Press, 81-115.

(1976) Elimination of quantifiers in the semantics of natural language by use of extended relation algebras. Revue Internationale de Philosophie, 117-118, 243-259.

(1974) On the grammar and model-theoretic semantics of children's noun phrases. Colloques Internationaux du C.N.R.S. Problèmes Actuels en Psycholinguistique, 206, 49-60.

With R. Smith and M. Léveillé. (1974) The French syntax of a child's noun phrases. Archives de Psychologie, 42, 207-269.

(1974) Model-theoretic semantics for natural language. In C. H. Heidrich (Ed.), Semantics and Communication. Amsterdam: North-Holland, 285-344.

(1974) The semantics of children's language. American Psychologist, 29, 103-114.

(1973) Congruence of meaning. Proceedings and Addresses of the American Philosophical Association, 46, 21-38.

(1973) Semantics of context-free fragments of natural languages. In K. J. J. Hintikka, J. M. E. Moravcsik, & P. Suppes (Eds.), Approaches to Natural Language. Dordrecht: Reidel, 370-394. German translation: Semantik für ein kontextfreies Fragment natürlicher Sprachen. In Studien zur Semantik, edited by S. Kanngiesser and G. Lingrün. Kronberg: Scriptor Verlag GmbH, 1974. pp. 98Ð135.

With S. Feldman. (1971) Young children's comprehension of logical connectives. Journal of Experimental Child Psychology, 12, 304-317

(1970) Probabilistic grammars for natural languages. Synthese, 22, 95-116. Reprinted in D. Davidson & G. Harman (Eds.), Semantics of Natural Language. Dordrecht: Reidel, 741-762.

(1969) Nagel's lectures on Dewey's logic. In S. Morgenbesser, P. Suppes, & M. White (Eds.), Philosophy, Science and Method: Essays in honor of Ernest Nagel. New York: St. Martin's Press, 2-25.

With N. Moler. (1968) Quantifier-free axioms for constructive plane geometry. Compositio Mathematica, 1968, 20, 143-152.

With R. D. Luce. (1968) Mathematics. In International Encyclopedia of the Social Sciences, Vol. 10. New York: Macmillan and Free Press, 65-76 Reprinted in International Encyclopedia of Statistics. New York: Free Press.

(1965) Logics appropriate to empirical theories. In J. W. Addison, L. Henkin, & A. Tarski (Eds.), Theory of Models. Amsterdam: North-Holland, 364-375. Reprinted in C. A. Hooker (Ed.), The Logico-algebraic Approach to Quantum Mechanics. Dordrecht: Reidel, 1975, 329-340. Rumanian translation in Gh. Enescu & C. Popa (Eds.), Logicas, tiint, ei. Bucharest: Editura Politica, 1970, 233-247.

With E. Crothers & R. Weir. (1964) Latency phenomena in prolonged learning of visual representations of Russian sounds. International Review of Applied Linguistics, 2, 205-217.

With S. Hill. (1964) First Course in Mathematical Logic. New York: Blaisdell, 274 pp. Spanish translation by E. L. Escardo, Introducci—n a La L—gica Matem‡tica. Barcelona: Editorial, S. A., 1968, 283 pp.

(1960) A comparison of the meaning and uses of models in mathematics and the empirical sciences. Synthese, 12, 287-301. Czechoslovakian translation: Srovn‡n’ v_znamu a pouzit’ modelu v matematice a v empirickych ved‡ch. In K. Berka & L. Tondl (Eds.), Teorie modelu a modelov‡n’. Dordrecht: Reidel, 1967, 208-222.

(1960) Problem analysis and ordinary language. Proceedings of the Twelfth International Congress of Philosophy, 4, 331-337.

(1960) Axiomatic set theory. New York: Van Nostrand, 265 pp. Spanish translation by H. A. Castillo, Teor’a Axiom‡tica de Conjuntos. Cali, Colombia: Editoriol Norma, 1968, 171 pp. Slightly revised edition published by Dover, New York, 1972, 267 pp.

(1957) Introduction to Logic. New York: Van Nostrand, 312 pp. Spanish translation by G. A. Carrasco: Introducci—n a la l—gica simb—lica. México: Compa–’a Editorial Continental, SA., 1966, 378 pp. Chinese translation by Fu-Tseng Liu. Buffalo Book Co. Ltd., Taiwan, R.O.C.