In mathematics, a consequence drawn by a deduction from a set of premises can also drawn by the same deduction from any larger set of premises. The deduction remains a deduction no matter how the axioms are increased. This is monotonic reasoning, much imitated in other, less certain, disciplines. The very nature of monotonic reasoning makes mathematical proofs permanent, independent of new info...

The automated deduction and model checking communities have developed techniques that are impressively e ective when applied to suitable problems. However, these problems seldom coincide exactly with those that arise in formal methods. Using small but realistic examples for illustration, I will argue that e ective deductive support for formal methods requires cooperation among di erent techniqu...

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in these systems compared to lengths in Frege proof systems. As an application we give a near-linear simulation of the proposition...

In first part of this course [28] we have laid the theoretical foundations for logic program specialisation, notably introducing the technique of partial deduction along with some basic techniques to automatically control it. In this part of the course we first present in Section 2 an advanced way of controlling polyvariance based upon characteristic trees. We then show in Section 3 how partial...

We propose the use of variable declarations in natural deduction. A variable declaration is a line in a derivation that introduces a new variable into the derivation. Semantically, it can be regarded as declaring that the variable denotes an element of the universe of discourse. Undeclared variables, in contrast, do not denote anything, and may not occur free in any formula in the derivation. A...

The home mortgage interest deduction creates incentives to buy more housing and to become a homeowner, and the case for the deduction rests on social benefits from housing consumption and homeownership. There is little evidence suggesting large externalities from the level of housing consumption, but there appear to be externalities from homeownership. Externalities from living around homeowner...