Introduction Rules Research Articles

Modal logics for communicating systems

Simple modal logics for Milner's SCCS and CCS are presented. We offer sound and complete axiomatizations of validity relative to these calculi as models. Also we present compositional proof systems for when a program satisfies a formula. These involve proof rules which are like Gentzen introduction rules except that there are also introduction rules for the program combinators of SCCS and CCS. The compositional rules for restriction (or hiding) and parallel combinators arise out of a simple semantic strategy.

Deduction theorems for weak implicational logics

The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as ‘the c’, ‘a (an) c’, ‘some c’, ‘any c’, and ‘every c’, where ‘c’ represents a common noun. These latter expressions are called quantifiers, and other expressions of the form ‘that c’ or ‘that c itself’, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that ‘Every man loves some woman’ is implied by, but does not imply, ‘Some woman is loved by every man’, since the latter is taken to mean the same as ‘Some woman is loved by all men’. Also, ‘Jack knows which woman came’ is implied by ‘Some woman is known by Jack to have come’, but not by ‘Jack knows that some woman came’.

On modal logic with propositional quantifiers

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

On modal logic with propositional quantifiers

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.

The fire underwriters' rules for safe introduction of acetylene gas generators

The fire underwriters' rules for safe introduction of acetylene gas generators