A semantical investigation on Brouwer-Zadeh logic

Conclusion In the standard approach to quantum mechanics, closed subspaces of a Hilbert space represent propositions. In the operational approach, closed subspaces are replaced by effects that represent a mathematical counterpart for properties which can be measured in a physical system. Effects are a proper generalization of closed subspaces. Effects determine a Brouwer-Zadeh poset which is not a lattice. However, such a poset can be embedded in a complete Brouwer-Zadeh lattice. From an intuitive point of view, one can say that these structures represent a natural logical abstraction from the structure of propositions of a quantum system. The logic that arises in this way is Brouwer-Zadeh logic. This paper shows that such a logic can be characterized by means of an algebraic and a Kripkean semantics. Finally, a strong completeness theorem for BZL is proved.     

A note on the decidability of a strong relevant logic

A modified filtrations argument is used to prove that the relevant logic S of [2] is decidable.     

Decidability,partial decidability and sharpness relation for L-subsets

If X is set and L a lattice, then an L-subset or fuzzy subset of X is any map from X to L, [11]. In this paper we extend some notions of recursivity theory to fuzzy set theory, in particular we define and examine the concept of almost decidability for L-subsets. Moreover, we examine the relationship between imprecision and decidability. Namely, we prove that there exist infinitely indeterminate L-subsets with no more precise decidable versions and classical subsets whose unique shaded decidable versions are the L-subsets almost-everywhere indeterminate.This research was supported by M. P. I. of Italy (60% and 40% 1986).     

Refutation systems in modal logic

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.Presented byJan Zygmunt     

The logic of unboundedly reactive systems

Summary Scientific theories often need to envision that a given output variable Y is jointly determined by all input variables of a certain kind _X that we can identify onlyas a kind without knowing all its specific instances or even how many of these there are, When the number of variables in _X is possibly infinite, the function by which they determine Y proves to be enormously enigmatic, epistemically, mathematically, and scientifically.     

Normative systems of discovery and logic of search

New computer systems of discovery create a research program for logic and philosophy of science. These systems consist of inference rules and control knowledge that guide the discovery process. Their paths of discovery are influenced by the available data and the discovery steps coincide with the justification of results. The discovery process can be described in terms of fundamental concepts of artificial intelligence such as heuristic search, and can also be interpreted in terms of logic. The traditional distinction that places studies of scientific discovery outside the philosophy of science, in psychology, sociology, or history, is no longer valid in view of the existence of computer systems of discovery. It becomes both reasonable and attractive to study the schemes of discovery in the same way as the criteria of justification were studied: empirically as facts, and logically as norms.     

Gentzenization and decidability of some contraction-less relevant logics

We adopt the terminology and bracketing conventions of [3], which in turn follows Dunn in [1], pp, 381–391, and Giambrone in [4]. We acknoledge the impetus given to this paper by Jonh Slaney who showed me a key to the dedidability argument, though the simplification used in this paper obviates the need for it.     

Axiomatisation and decidability ofF andP in cyclical time

We present a Hilert style axiomatisation for the set of formulas in the temporal language withF andP which are valid over non-transitive cyclical flows of time.We also give a simpler axiomatisation using the slightly controversial irreflexivity rule and go on to prove the decidability of any temporal logic over cyclical time provided it uses only connectives with first-order tables.