Alongside theoretical logic, which systematises the proof schemata of theoretical truths, one can systematise the schemata of problem-solving, e.g. those of geometric construction problems. Then, corresponding to the principle of the syllogism, we find for example, the following principle: If we can reduce the solution of b to that of a, and reduce the solution of c to that of b, then we can al...

This work is a revision of the False Dilemma Fallacy (FDF). The formalized model (FM)of this fallacy has as its centerpiece valid disjunctive syllogism, but premise presumed to be false, thus making argument unsound. Our revised (FM2.0) focuses on formal structure by comparing given vs. real argument, which unsound because invalidity. approach we believe more pedagogically useful and better exp...

Mental models theorists (e.g., Johnson-Laird & Byrne, 1991) suggest that syllogism terms are represented in working memory as ‘abstract tokens’. However, the role that working memory sub-systems and prior knowledge play in the representation and processing of such terms is poorly specified. Two experiments are reported in which the representational distinctiveness of syllogism terms was manipul...

Berit Brogaard and Joe Salerno (2008) have defended the validity of counterfactual hypothetical syllogism (CHS) within the Stalnaker-Lewis account. Whenever the premisses of an instance of CHS are non-vacuosly true, a shift in context has occurred. Hence the standard counterexamples to CHS suffer from context failure. Charles Cross (2011) rejects this argument as irreconcilable with the Stalnak...

We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. To make the development more natural,...

Gender, Economic Development and Islam: A Perspective from France Muslims do less well on the French labor market than their non Muslim counterparts. One explanation for this relative failure can be characterized by the following syllogism: (1) the empowerment of women is a sine qua non for economic progress; (2) in-group norms among Muslims do not empower women; and hence (3) Muslim communitie...

Uncertain entailment is a methodology for calculating the truth value of an uncertain formula via the maximum uncertainty principle when the truth values of other uncertain formulas are given. In order to find the truth value of additional formula, this paper will introduce an entailment model. As applications of uncertain entailment, this paper will also discuss modus ponens, modus tollens, an...

There are two major traditions in formal logic: term logic and propo-sitional/predicate logic, exempliied respectively by the Syllogism of Aristotle and the First-Order Predicate Logic founded by Frege, Rus-sell, and Whitehead. Term logic is diierent from predicate logic in both its knowledge representation language and its inference rules. Term logic represents knowledge in subject{predicate s...