To the memory of Prof. Grigori Mints, Stanford UniversityBorn: June 7, 1939, St. Petersburg, RussiaDied: May 29, 2014, Palo Alto, California.

A history of the logic of action is outlined, beginning with St Anselm. Five modern authors are discussed in some detail: von Wright, Fitch, Kanger, Chellas and Pratt.

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...) derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete. (shrink)

We consider a quantifier-free language in which there are terms as well as formulas. The proposition-forming propositional operators are the usual ones, and the term-making term operators are the usual lattice theoretical ones. In addition there is a formula-making term operator, does. We study a new logic in which does is claimed to approximate some features of the informal concept the agent performs the action.

Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these errors and (...) presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism. (shrink)

Whileprocess andaction are fundamental notions, in ubiquitous use, they lack satisfactory logical treatment in two critical respects: in analyses of the fundamentals themselves and in logical development. For what treatment they have so far received, under classical systematisation, leaves significant lacunae and induces much paradox. A relevant logical relocation, carried through in detail here, removes such problems, and provides solid ground-work for a satisfactory treatment.Firstly, as to fundamentals: processes should be explicated, so it is argued, as certain sorts of (time) (...) directed functions (from inputs to outputs); thus they can be represented through certain ordered pairs of relations. Significant logical structures they can enter into are investigated: notably, process lattice and coupled logics, and a generalized category theory (tolerating nonassociativity of composition). (shrink)