A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. (shrink)

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, (...) have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization–Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models.Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

According to classical arguments, language learning is both facilitated and constrained by cognitive biases. These biases are reflected in linguistic typology—the distribution of linguistic patterns across the world's languages—and can be probed with artificial grammar experiments on child and adult learners. Beginning with a widely successful approach to typology (Optimality Theory), and adapting techniques from computational approaches to statistical learning, we develop a Bayesian model of cognitive biases and show that it accounts for the detailed pattern of results of artificial (...) grammar experiments on noun-phrase word order (Culbertson, Smolensky, & Legendre, 2012). Our proposal has several novel properties that distinguish it from prior work in the domains of linguistic theory, computational cognitive science, and machine learning. This study illustrates how ideas from these domains can be synthesized into a model of language learning in which biases range in strength from hard (absolute) to soft (statistical), and in which language-specific and domain-general biases combine to account for data from the macro-level scale of typological distribution to the micro-level scale of learning by individuals. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases (...) of the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)

In this article, I survey the integrated connectionist/symbolic (ICS) cognitive architecture in which higher cognition must be formally characterized on two levels of description. At the microlevel, parallel distributed processing (PDP) characterizes mental processing; this PDP system has special organization in virtue of which it can be characterized at the macrolevel as a kind of symbolic computational system. The symbolic system inherits certain properties from its PDP substrate; the symbolic functions computed constitute optimization of a well-formedness measure called Harmony. The (...) most important outgrowth of the ICS research program is optimality theory (Prince & Smolensky, 1993/2004), an optimization based grammatical theory that provides a formal theory of cross-linguistic typology. Linguistically, Harmony maximization corresponds to minimization of markedness or structural ill-formedness. Cognitive explanation in ICS requires the collaboration of symbolic and connectionist principles. ICS is developed in detail in Smolensky and Legendre (2006a); this article is a précis of and guide to those volumes. (shrink)

Generative linguistics' search for linguistic universals (1) is not comparable to the vague explanatory suggestions of the article; (2) clearly merits a more central place than linguistic typology in cognitive science; (3) is fundamentally untouched by the article's empirical arguments; (4) best explains the important facts of linguistic diversity; and (5) illuminates the dominant component of language's nature: biology.

The target article offers an analysis of the categorization of kin types and empirical evidence that cross-cultural universals may be amenable to OT explanation. Since the analysis concerns the structuring of conceptual categories rather than the use of words, it differs from previous OT analyses in lexical semantics in what is considered to be the input and output of optimization.

Young French children freely produce subject pronouns by the age of 2. However, by age 2 and a half they fail to interpret 3rd person pronouns in an experimental setting designed to select a referent among three participants (speaker, hearer, and other). No such problems are found with 1st and 2nd person pronouns. We formalize our analysis of these empirical results in terms of direction-sensitive optimizations, showing that uni-directionality of optimization, when combined with non-adult-like constraint rankings, explains the general acquisition (...) pattern of 3rd person pronouns. Building on a specific analysis of assigning 3rd person reference by computing over alternatives (Heim 1991 ), we show that adult interpretation does not require bidirectional OT although it is fully compatible with it. What matters for comprehension in the domain investigated here is constraint ranking. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

Case (a) has been familiar for a long time, and is supported by a fair amount of historical evidence (Kiparsky 1968, 1973). It was adopted by NGG (Vennemann 1972, Hooper 1976) and by Natural Phonology (Stampe 1972/1980). Prince & Smolensky 1993 dub it lexicon optimization, and show that it is a consequence of basic assumptions of OT.

This self-contained treatise, originally published in 1947 by Holt, Rinehart and Winston, examines fundamental features of nature in order to lay the groundwork for providing a solution to the major problems of ethics.

In The Conditions for Ethical Chemical Restraint, Crutchfield and Redinger (2024) propose ethical standards for the use of chemical restraints, which they consider normatively distinct from physica...

v. 1. 1955-1960.--v. 2. 1960-1964.--v. 3. March-November 1964.--v. 4. November 26, 1964-September 2, 1965.--v. 5. September 3, 1965-August 27, 1968.--v. 6. August 28, 1968-May 22, 1971.--v. 7. April 13, 1975-June 21, 1976.--v. 7, pt. 2. September 17, 1977-February 26, 1978.--v. 8. April 28, 1978-July 28, 1980 -- v. 9. August 16, 1980-March 15, 1984 -- v. 11. January 19, 1986-May 27, 1987.

The options in a decision problem generally have outcomes with common features. Putting aside the common features simplifies deliberations, but the simplification requires a philosophical justification that this book provides.

In the first part of this paper some general theses concerning the difference between logic and mathematics are defended. In the second part four different views for a possible demarcation between logic and mathematics are stated.

Schelling und Hegel benutzen in ihren philosophischen Texten mathematische und naturwissenschaftliche Modelle wie Unendlichkeit oder Gleichgewicht. Die Strukturen dieser Begriffe liefern einen Massstab fur den Vergleich der Positionen Schellings und Hegels, der fur Schellings Identitatsphilosophie und Hegels erste Jenaer Schriften durchgefuhrt wird. Als wichtigstes Resultat kann eine grundlegende Differenz zwischen beiden Positionen bereits um 1801 nachgewiesen und gezeigt werden, dass diese auf einer unterschiedlichen Auffassung der Rolle des Absoluten beruht.

The first book-length study of a leading tenth-century Ismaili theoretician Abu Ya'qub al-Sijistani.