Local Equational Logic II
نویسنده
چکیده
A logic may be called local if each model may be used to deene the truth. In the proposition calculus each boolean algebra deene the truth by its greatest element. In the equational logic the equality between the algebra elements deene the truth. In the clause Horn logic the truth is given by the interpretation of the predicats in the model. We give a categorial framework for these logics and we show that the main results may be proved.
منابع مشابه
An Equation-Based Classical Logic
We propose and study a logic able to state and reason about equational constraints, by combining aspects of classical propositional logic, equational logic, and quantifiers. The logic has a classical structure over an algebraic base, and a form of universal quantification distinguishing between local and global validity of equational constraints. We present a sound and complete axiomatization f...
متن کاملOn the mathematical synthesis of equational logics
Birkhoff [1935] initiated the general study of algebraic structure. Importantly for our concerns here, his development was from (universal) algebra to (equational) logic. Birkhoff’s starting point was the informal conception of algebra based on familiar concrete examples. Abstracting from these, he introduced the concepts of signature and equational presentation, and thereby formalised what is ...
متن کاملCategory-based Semantics for Equational and Constraint Logic Programming
This thesis proposes a general framework for equational logic programming, called catf:gory based equational logic by placing the general principles underlying the design of the pro gramming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfy ing certain natural conditions; completeness i...
متن کاملProving Ground Confluence of Equational Specifications Modulo Axioms
Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critic...
متن کاملProof of Correctness of Object Representations 3
1.1 Introduction This paper presents an algebraic account of implementation that is applicable to the object paradigm. The key to its applicability is the notion of state: objects have local states that are observable only through their outputs. That is, objects may be viewed as abstract machines with hidden local state (as in 9]). Consequently, a correct implementation need only have the requi...
متن کامل