Sentence examples for default conditional from inspiring English sources

The truth-conditions of the default conditional and the definition of nonmonotonic consequence can be fine-tuned to match many of our intuitions, but in the end of the day, the theory of Commonsense Entailment offers no simple answer to the question of what its conditional or its consequence relation are supposed (ideally) to represent.

In particular, they require the default conditional operator, ⇒, to have wide scope in every formula in which it appears.

For example, in representing undercutting defeaters, it would be very natural to use a negated default conditional of the form ¬((p & q) ⇒ r) to signify that q defeats p as a prima facie reason for r.

A default conditional (p ⇒ q) is true in a world w (in such a model) just in case all of the most normal p worlds (from w's perspective) are worlds in which q is also true.

When this insight is applied to the nonmonotonic logic of extreme probabilities, we can use causal information to identify which defaults function independently of others: that is, we can decide when the fact that one default conditional has an exception is irrelevant to the question of whether a second conditional is also violated (see Koons 2000, 320 323).

We can then distinguish between a default conditional's following with logical necessity from a default theory and its following defeasibly from that same theory.

By making use of a theory of default conditionals, here given by System Z, we isolate minimal sets of defaults with specificity conflicts.

Default conditionals are not allowed to be nested within other default conditionals, or within the scope of the usual Boolean operators of propositional logic (negation, conjunction, disjunction, material conditional).

It permits the arbitrary nesting of default conditionals within other logical operators, and it can be used to represent undercutting defeaters, through the use of negated defaults (Asher and Mao 2001).

However, if we replace the first two default conditionals by the single default, Swedes are normally both tall and fair, then the conclusion no longer follows, despite the fact that the new conditional is logically equivalent to the conjunction of the two original conditionals.

Logics of extreme probability (beginning with the work of Ernest Adams) did not permit the nesting of default conditionals for this reason: the conditionals were supposed to represent something like subjective conditional probabilities of the agent, to which the agent was supposed to have perfect introspective access.