In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of p...

For those who have never taken the trouble to consider ways and methods of thinking and who wish to know of a readable and interesting introduction to the subject this small book of Canon Dewar's can be confidently recommended. Its three sections cover a great deal of ground. The first is concerned with different types of thinking and with the rules of the syllogism. The second calls attention ...

Internal syntactic operations on diagrams play a key role in accounting for efficacy of diagram use in reasoning. However, it is often held that in the case of complex deductive reasoning, diagrams can serve merely as an auxiliary source of information in interpreting sentences or constructing models. Based on experiments comparing subjects’ performances in syllogism solving where logic diagram...

Peterson’s Intermediate Syllogisms, generalizing Aristotelian syllogisms by intermediate quantifiers ‘Many’, ‘Most’ and ‘Almost all’, are studied. It is demonstrated that, by associating certain values V, W and U on standard Lukasiewicz MV–algebra with the first and second premise and the conclusion, respectively, the validity of a corresponding intermediate syllogism is determined by a simple ...

The relationship between metaphor and the practice of utilization in therapy and hypnosis can be seen as dependent on metaphor's role in structuring experience. The work of Gregory Bateson and others is used to illustrate how metaphor functions. Bateson's comparison of two forms of syllogistic logic provides a background for distinguishing between the experiential effects of metaphor in contras...

In this paper we use an interpretation of fuzzy if-then rules to consider the notion of fixed points that are also called fix mundis in the literature invented by Fathi/Temme. We review some known results on fixed points of fuzzy ifthen rules and add more new ones and bring up the notion of fixed points in fuzzy chaining syllogism and we obtain new and interesting conclusions. Finally we bring ...

We give some simple examples of applying the well-known elementary probability theory inequalities and properties in field logical argumentation. A probabilistic version hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, B→C have probabilities a, b, c, r, s, respectively, then for p A→C, we f(a,b,c,r,s)≤p≤g(a,b,c,r,s), functions f g given parameters. In this pape...

Adopting a different method from the previous scholars, this article deduces remaining 23 valid syllogisms just taking syllogism AEE-4 as basic axiom. The idea of study is follows: firstly, make full use trichotomy structure categorical propositions to formalize syllogisms. Then, advantage deductive rules in classical propositional logic and facts generalized quantifier theory, we deduce by one...

We consider an algorithmic approach for revising inconsistent data and restoring its consistency. This approach detects the \spoiled" part of the data (i.e., the set of assertions that cause inconsistency), deletes it from the knowledge-base, and then draws classical conclusions from the \recovered" information. The essence of this approach is its coherence with the original (possibly inconsist...

The main aim of this study was to examine whether people understand indicative conditionals on the basis of syntactic factors or on the basis of subjective conditional probability. The second aim was to investigate whether the conditional probability of q given p depends on the antecedent and consequent sizes or derives from inductive processes leading to establish a link of plausible cooccurre...