This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had (...) no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain. (shrink)

In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.

Most theories of deduction have assumed that linguistic processes transduce from language into an internal representation and back again, and that non-linguistic processes are central to deduction itself. In this article it is proposed that for deduction tasks for which the necessary information is provided verbally, the heart of deduction for untrained participants involves repeatedly reencoding the problem, a type of behavior referred to here as verbal reasoning. It is shown that model theory accounts of behavior on most deduction tasks (...) are consistent with verbal reasoning and that verbal reasoning can account for detailed behavior in a single task; a computational model of syllogistic reasoning—VR—based on linguistic mechanisms is presented. VR models all of the standard phenomena, makes a number of accurate novel predictions, and fits the behavior of individual participants with an accuracy that rivals their own test–retest reliability. (shrink)

Johnson-Laird and Byrne present a theory of conditional inference based upon the manipulation of mental models. In the present paper, the theory is critically examined with regard to its ability to account for psychological data, principally with respect to the rate at which people draw the four basic inferences of modus ponens, denial of the antecedent, affirmation of the consequent and modus tollens. It is argued first that the theory is unclear in its definition and in particular with regard to (...) predictions of problem difficulty. Clarification and specification of principles are consequently provided here. Next, it is argued that there are a number of phenomena in the conditional reasoning literature for which the theory cannot account in its present form. Specifically, the relatively frequency of DA and AC inferences on affirmative conditionals is not as predicted by the theory, differences occur between inferences on if then and only if rules beyond the capacity of the theory to explain and there is no account of the “negative conclusion bias” observed when negated components are introduced into the rules. A number of revisions to the mental model theory of conditional reasoning are proposed in order to account for these findings. (shrink)

The mental model theory postulates that reasoners build models of the situations described in premises. A conclusion is possible if it holds in at least one model of the premises; it is probable if it holds in most of the models; and it is necessary if it holds in all of the models. The theory also postulates that reasoners represent as little information as possible in explicit models and, in particular, that they represent only information about what is true. One (...) unexpected consequence of this assumption is that there should be a category of illusory inferences: they will have conclusions that seem obvious, but that are wholly erroneous. Experiment 1 established the existence of such illusory inferences about probabilities. Overall, 88% of the intelligent adult subjects chose as more probable an outcome that was impossible for at least one of the illusory problems. Experiment 2 corroborated the phenomenon and showed that illusory inferences include a wide variety of problems. Finally, the paper argues that current theories based on formal rules of inference are unlikely to be able to explain the illusions. (shrink)

This volume succeeds the same authors' well-known An Introduction to Modal Logic and A Companion to Modal Logic. We designate the three books and their authors NIML, IML, CML and H&C respectively. Sadly, George Hughes died partway through the writing of NIML.