Search results for "Syllogism"
showing 3 items of 13 documents
Probabilistic semantics for categorical syllogisms of Figure II
2018
A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of \(\bar{P}|S\) from the premise set \(\{M|P,\bar{M}|S\}\) is not informative, we add \(p(S|(S \vee P))>0\) as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the…
The Syllogistic with Unity
2011
We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.
The Relational Syllogistic Revisited
2013
The relational syllogistic is an extension of the language of Classical syllogisms in which predicates are allowed to feature transitive verbs with quantified objects. It is known that the relational syllogistic does not admit a finite set of syllogism-like rules whose associated (direct) derivation relation is sound and complete. We present a modest ex- tension of this language which does.