A model of deductive reasoning requires two components. The performance component comprises programs for comprehending premises and for constructing a line of reasoning. The logical component, the subject of the article, consists of some logical vocabulary and a repertory of elementary deductive steps. This component is specified for prepositional reasoning by presenting a logic in which the connectives capture essential syntactic and semantic properties of the corresponding English words (unlike the connectives of standard logic). The repertory of deductive steps is defined through inference rule schemata. The system has the same "theorems" as standard prepositional logic but different foundations. However, people lack explicit knowledge of their inference rule schemata and, therefore, are unaware of what can be proved from them. This ignorance of the entailments of their own system, coupled with the difference in foundations, explains the differences between natural and standard logic, especially in relation to or and if, which are discussed in some detail.This article presents a system of logic that claims to be the logic that people use in prepositional reasoning. The use of the term "natural" to claim that a logic is psychologically valid goes back to Gentzen (1935Gentzen ( /1964, whose system of "natural deduction" was motivated I am grateful to my brother, David Braine, of the Department of Logic, University of Aberdeen, for informal instruction on a variety of issues in logic and for drawing my attention to the existence of Gentzen's work. I am also grateful to Jack Barense, of Absecon, New Jersey, for a critical reading of an earlier draft, for discussion of the relations between if-then and entailment, and for much general discussion, some of which is acknowledged in the text. Of course, neither of these philosophers is to be blamed if their instruction was not extensive enough. I also thank Rachel Falmagne for comments and suggestions that improved the article.Requests for reprints should be sent to Martin

The theory has 3 parts: (a) A lexical entry defines the information about if in semantic memory; its core comprises 2 inference schemas, Modus Ponens and a schema for Conditional Proof; the latter operates under a constraint that explains differences between (/and the material conditional of standard logic, (b) A propositional-logic reasoning program specifies a routine for reasoning from information as interpreted to a conclusion, (c) A set of pragmatic principles governs how an ;/ sentence is likely to be interpreted in context. The reasoning program and the pragmatic principles are independently motivated. The theory accounts well for relevant research data-explaining inferences, fallacies, truth judgments, and comprehension errors-and both schemas appear to be available early to children. Other psychological theories are incomplete. Stalnaker's philosophical theory is more complex and begs questions about how possible worlds are apprehended.

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