Consider syllogisms in which fraction (percentage) quantifiers are permitted in addition to universal and particular quantificrs, and then include further quantifiers which are modifications of such fractions (such as "almost ½ the S are P" and "Much more than ½ the S are P"). Could a syllogistic system containing such additional categorical forms be coherent? Thompson's attempt (1986) to give rules for determining validity of such syllogisms has failed; cf. Carnes & Peterson (forthcoming) for proofs of the unsoundness and incompleteness (...) of Thompson's rules. Building on Peterson (1985), the coherence of such a syllogistic can, however, be demonstrated with an algebra which provides its semantics; e.g., "almost ¾ the S arc P'" is represented as " -(3(SP) » SP)". (shrink)

In this publication we continue the study of fuzzy Peterson’s syllogisms. While in the previous publication we focused on verifying the validity of these syllogisms using the construction of formal proofs and semantic verification, in this publication we focus on verifying the validity of syllogisms using Peterson’s rules based on grades.

En esta contribución proponemos una representación de un fragmento de la silogística estadística de Thompson usando la lógica de términos de Sommers. El resultado es una interpretación terminista de la silogística estadística.

In the analysis of syllogistic reasoning, a type of inference patternbased on the chaining of terms through quantified statements, two interpretationsabout them can be found in the literature. One is the so-called set-based interpretation,which assumes that quantified statements and syllogisms talk aboutquantity-relationships between sets. The other one, the so-called conditionalinterpretation, assumes that they talk about conditional propositions and howstrong are the links between the antecedent and the consequent. In this paper,we expose both models and formulate three relevant questions to be (...) taken intoaccount for a further development of this type of reasoning. (shrink)