0000000000772462
AUTHOR
N Pfeifer
Probabilistic inference and syllogisms
Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All S are P ” and “At least one S is P ” and their respective negated versions. We will discuss probabilistic notions of the existential import and the basic sentences type. We will develop an intuitively plausible version of the syllogisms that is able to deal with uncertainty, exceptions and nonmonotonicity. We will develop a new semantics for categorical syllogisms that is based on subjective probability. Specifically, we propose de Finetti’s principle of coherence and its generalization to lower and upper conditional probabilities as the fundamental corner ston…
Probabilistic interpretations of the square of opposition
We investigate the square of opposition from a probabilistic point of view. Probability allows for dealing with exceptions and uncertainty. We will interpret the corners of the square by means of (precise or imprecise) conditional probability assessments. They will be defined within the framework of coherence, which originally goes back to de Finetti. In this framework probabilities are conceived as degrees of belief, where conditional probability is defined as a primitive concept. Coherence allows for dealing with partial and imprecise assessments. Moreover, the coherence approach is especially suitable for dealing with zero antecedent probabilities (i.e., here conditioning events may have…