In ordinary rst order logic, a valid inference in a language L is one in which the conclusion is true in every model of the language in which the premises are true. To accommodate inductive/uncertain/probabilistic/nonmonotonic inference, we weaken that demand to the demand that the conclusion be true in a large proportion of the models in which the relevant premises are true. More generally, we...

We show how and why it makes sense to use a relational formalisation instead of the usual functional one in the treatment of term graphs. Special attention is paid to term graphs with bound variables, that have, to our knowledge, never been formalised with such a generality before. Besides the novel treatment of term graphs themselves, we present an innovative relational homomorphism concept th...