Normal form of formulas of pure hybrid logic

Daiva Aleknavičiūtė,Stanislovas Norgėla

doi:10.15388/lmr.2007.24225

Abstract

In this paper,we study a transformationof pure hybrid logic formulae,which do not have binding operator, into an equivalent normal form, which does not have any satisfiability operators in the scope of another satisfiability operator.

Highlights

Lets extend multimodal logic with new symbols which we will call nominals
Nominals are counted as atomic formulae of the hybrid logics
We will look at formulae of pure hybrid logics, i.e., hybrid logics without propositional symbols

Summary

Introduction

Lets extend multimodal logic with new symbols which we will call nominals. Elements of a new set NOM = {i, j, ...} have to distinct from propositional symbols from set PROP = {p, q, ...}. Nominals are counted as atomic formulae of the hybrid logics. Symbols , ⊥ (truth, false) are atomic formulae. Once we have names for the nodes, we can add another operator, which would allow us to declare that formula F is valid at node i. Formula ↓ x.F has meaning: “F is valid in all nodes which are currently examined.

Results

Conclusion