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Bulletin of the Section of Logic > 2020 > 49 > 3 > 291-324
In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear)...
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We introduce an efficient decision procedure for the theory of equality based on finite instantiations. When using the finite instantiations method, it is a common practice to take a range of [1..n] (where n is the number of input non-Boolean variables) as the range for all non-Boolean variables, resulting in a state-space of n n . Although various attempts to minimize...
chapter
Equality Logic with uninterpreted functions is used for proving the equivalense or refinement between systems (hardware verification, compiler translation, etc). Current approaches for deciding this type of formulas use a transformation of an equality formula to the propositional one of larger size, and then any standard SAT checker can be applied. We give an approach for deciding satisfiability of...
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Journal of Applied Logic > 2012 > 10 > 2 > 199-217
There are currently no fewer than four dedicated logics for equality reasoning over nominal sets: nominal algebra, nominal equational logic, nominal equational logic with equality only, and permissive-nominal algebra.In this survey and research paper we present these logics side-by-side in a common notation, survey their similarities and differences, discuss their proof- and model-theories, and discuss...
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We present a novel abstraction-based approach to controller synthesis based on the use of a logic with uninter-preted functions, arrays, equality, and limited quantification. Extending the Burch-Dill paradigm for the verification of pipelined processors, we show how to use this logic to synthesize the Boolean control of a pipelined circuit, using a sequential version as the specification. Thus, we...
