The logic of inexact concepts

  title={The logic of inexact concepts},
  author={Joseph A. Goguen},
  • J. Goguen
  • Published 2004
  • Computer Science
  • Synthese
The 'hard' sciences, such as physics and chemistry, construct exact mathematical models of empirical phenomena, and then use these models to make predictions. Certain aspects of reality always escape such models, and we look hopefully to future refinements. But sometimes there is an elusive fuzziness, a readjustment to context, or an effect of observer upon observed. These phenomena are particularly indigenous to natural language, and are common in the 'soft' sciences, such as biology and… Expand
An in uential tradition in philosophy equates the meaning of a sentence to its truth
An in uential view in philosophy and linguistics equates the meaning of a sentence to the conditions under which it is true. But it has been argued that this truth-conditional view is too rigid, andExpand
What Is a Concept?
The purpose of this paper is to explore the nature of difficulties of living human concepts, by drawing on ideas from contemporary cognitive science, sociology, computer science, and logic, and suggests approaches for dealing with these difficulties, again drawing on diverse literatures, particularly ideas of Peirce and Latour. Expand
Truth and entailment for a vague quantifier
We wish to study the logic of propositions of the form, 'almost all A's are B's' (or more generally 'almost all n-tuples from A satisfy an n-ary relation B'). Such propositions are encountered moreExpand
Intuitionism and the Sorites Paradox
  • Crispin Wright
  • Philosophy
  • The Riddle of Vagueness
  • 2021
This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vagueExpand
Jesuit Probabilistic Logic between Scholastic and Academic Philosophy
There is a well-documented paradigm-shift in eighteenth century Jesuit philosophy and science, at the very least in Central Europe: traditional scholastic version(s) of Aristotelianism were replacedExpand
Random Predicate Logic I : A Probabilistic Approach to Vagueness
1. Old-Fangled Predicates Predicates are supposed to slice reality neatly in two halves, one for which the predicate holds, the other for which it fails. Yet far from being razors, predicates tend toExpand
A Fuzzy Set Approach to Modifiers and Vagueness in Natural Language
Recent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that the meaningsExpand
The Genesis of Fuzzy Sets and Systems - Aspects in Science and Philosophy
  • R. Seising
  • Philosophy, Computer Science
  • Fifty Years of Fuzzy Logic and its Applications
  • 2015
This chapter deals with developments in the history of philosophy, logic, and mathematics during the time before and up to the beginning of fuzzy logic and it also gives a view of its first application in control theory. Expand
From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions
  • L. Zadeh
  • Computer Science, Medicine
  • Logic, Thought and Action
  • 2005
An outline of a methodology for reasoning and computing with perceptions rather than measurements is presented, a theory which may have an important bearing on how humans make--and machines might make--perception-based rational decisions in an environment of imprecision, uncertainty, and partial truth. Expand
Formalizing Approximate Objects and Theories: Some Initial Results
This paper introduces some preliminary formalizations of the approximate entities of [McCarthy, 2000], and develops a simple ontology, with minimal philosophical assumptions, in which to cast their formalization. Expand


Vagueness. An Exercise in Logical Analysis
  • M. Black
  • Mathematics
  • Philosophy of Science
  • 1937
/^scientific theories are ostensibly expressed in terms ( 1 ,~ ,of objects never encountered in experience. The line (7 traced by a draughtsman, no matter how accurate, 'i is seen beneath theExpand
The Philosophy of Mathematics
  • E. Bell
  • Philosophy, Computer Science
  • 1950
The three “schools” of mathematical philosophy which have emerged in the twentieth century: Logic ism, Formalism, and Intuitionism are discussed. Expand
An Introduction to the Theory of Numbers
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.Expand
Fuzzy sets and systems
  • L. Zadeh
  • Mathematics, Computer Science
  • 1990
The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do notExpand
Fuzzy Algorithms
  • L. Zadeh
  • Computer Science
  • Inf. Control.
  • 1968
A fuzzy algorithm is introduced which, though fuzzy rather than precise in nature, may eventually prove to be of use in a wide variety of problems relating to information processing, control, pattern recognition, system identification, artificial intelligence and, more generally, decision processes involving incomplete or uncertain data. Expand
Reasoning with Loose Concepts
A Man whose height is four feet is short; adding one tenthof an inch to a short man's height leaves him short; therefore, a man whose height is four feet and one tenth of an inch is short. Now beginExpand
Some studies in machine learning using the game of checkers
  • A. Samuel
  • Computer Science
  • IBM J. Res. Dev.
  • 2000
Enough work has been done to verify the fact that a computer can be programmed so that it will learn to play a better game of checkers than can be played by the person who wrote the program. Expand
Probability measures of Fuzzy events
In probability theory [I], an event, A, is a member of a a-field, CY, of subsets of a sample space ~2. A probability measure, P, is a normed measure over a measurable space (Q, GY); that is, P is aExpand
Abstraction and pattern classification
Abstract : This is a preliminary paper in which the authors discuss a general framework for the treatment of pattern-recognition problems. They make precise the notion of a 'fuzzy' set. Then theyExpand
Some studies in machine learning using the game of checkers. II: recent progress
Full use is made of the so called "alpha-beta" pruning and several forms of forward pruning to restrict the spread of the move tree and to permit the program to look ahead to a much greater depth than it otherwise could do. Expand