A Hilbert-Style Axiomatisation for Equational Hybrid Logic

A Hilbert-Style Axiomatisation for Equational Hybrid Logic

This paper introduces an axiomatisation for equational hybrid logic based on previous axiomatizations and natural deduction systems for propositional and firstorder hybrid logic. Its soundness and completeness is discussed. This work is part of a broader research project on the development a general proof calculus for hybrid logics.

A Hilbert-style axiomatization of higher-order intuitionistic logic

Two Hilbert calculi for higher-order intuitionistic logic (or theory of types) are introduced. The first is defined in a language that uses just exponential types of power type, and corresponds to Bell’s local set theory. The second one is defined in a language with arbitrary functional types and correspond to Church’s simple type theory. We show that both systems are sound and complete with re...

Hilbert-Style Axiomatization for Hybrid XPath with Data

In this paper we introduce a sound and complete axiomatization for XPath with data constraints extended with hybrid operators. First, we define HXPath=(↑↓), an extension of vertical XPath with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=(↑↓), and we prove it is complete with respect to the class of abstract data trees, i.e., data trees in which data val...

Equational Logic and Equational Theories of Algebras

Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic

We show that the generalized variant of formal systems where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational logic, many-sorted equational logic, and Horn logic with equality are likewise reflective. These resu...