𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Categorical abstract algebraic logic: The Diagram and the Reduction Operator Lemmas

✍ Scribed by George Voutsadakis

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
242 KB
Volume
53
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The study of structure systems, an abstraction of the concept of first‐order structures, is continued. Structure systems have algebraic systems as their algebraic reducts and their relational component consists of a collection of relation systems on the underlying functors. An analog of the expansion of a first‐order structure by constants is presented. Furthermore, analogs of the Diagram Lemma and the Reduction Operator Lemma from the theory of equality‐free first‐order structures are provided in the framework of structure systems. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Categorical abstract algebraic logic: Th
Categorical abstract algebraic logic: The categorical Suszko operator
✍ George Voutsadakis 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 229 KB

## Abstract Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibn

Categorical abstract algebraic logic: Th
Categorical abstract algebraic logic: The criterion for deductive equivalence
✍ George Voutsadakis 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract Equivalent deductive systems were introduced in [4] with the goal of treating 1‐deductive systems and algebraic 2‐deductive systems in a uniform way. Results of [3], appropriately translated and strengthened, show that two deductive systems over the same language type are equivalent if

Categorical abstract algebraic logic: Ge
Categorical abstract algebraic logic: Gentzen π -institutions and the deduction-detachment property
✍ George Voutsadakis 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB

Given a π-institution I, a hierarchy of π-institutions I (n) is constructed, for n ≥ 1. We call I (n) the n-th order counterpart of I. The second-order counterpart of a deductive π-institution is a Gentzen π-institution, i. e. a π-institution associated with a structural Gentzen system in a canonica

Categorical abstract algebraic logic: Th
Categorical abstract algebraic logic: The largest theory system included in a theory family
✍ George Voutsadakis 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 116 KB

## Abstract In this note, it is shown that, given a __π__ ‐institution ℐ = 〈**Sign**, SEN, __C__ 〉, with __N__ a category of natural transformations on SEN, every theory family __T__ of ℐ includes a unique largest theory system $ \overleftarrow T $ of ℐ. $ \overleftarrow T $ satisfies the important