title: Immediate inferences from quantified assertions.
abstract: We propose a theory of immediate inferences from assertions containing a single quantifier, such as: All of the artists are bakers; therefore, some of the bakers are artists. The theory is based on mental models and is implemented in a computer program, mReasoner. It predicts three main levels of increasing difficulty: (a) immediate inferences in which the premise and conclusion have identical meanings; (b) those in which the initial mental model of the premise yields the correct conclusion; and (c) those in which only an alternative to the initial model establishes the correct conclusion. These levels of difficulty were corroborated for inferences to necessary conclusions (in a reanalysis of data from Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior, 22, 535-546), for inferences to modal conclusions, such as, it is possible that all of the bakers are artists (Experiment 1), for inferences with unorthodox quantifiers, such as, most of the artists (Experiment 2), and for inferences about the consistency of pairs of quantified assertions (Experiment 3). The theory also includes three parameters in a stochastic system that predicted quantitative differences in accuracy within the three main sorts of inference.
authors.affiliation: a Navy Center for Applied Research in Artificial Intelligence , Naval Research Laboratory , Washington , DC , USA.
authors.forename: Sangeet
authors.initials: S
authors.lastname: Khemlani
authors.forename: Max
authors.initials: M
authors.lastname: Lotstein
authors.forename: J Gregory
authors.initials: JG
authors.lastname: Trafton
authors.forename: P N
authors.initials: PN
authors.lastname: Johnson-Laird
mesh_terms: D000465:Algorithms; D005260:Female; D006801:Humans; D033182:Intention; D007600:Judgment; D008128:Logic; D008297:Male; D008960:Models, Psychological; D011340:Problem Solving / Q000502:physiology*; D013269:Stochastic Processes; D013850:Thinking / Q000502:physiology*
keywords: Logic; Mental models; Quantifiers; Reasoning; Syllogisms