Abstract

When it comes to the writing of a new logic program or theory, it is of great importance to obtain a concise and minimal representation, for simplicity and ease of interpretation reasons. There are already a few methods and many tools, such as Karnaugh Maps or the Quine-McCluskey method, as well as their numerous software implementations, that solve this minimization problem in Boolean logic. This is not the case for Here-and-There logic, also called three-valued logic. Even though there are theoretical minimization methods for logic theories and programs, there aren’t any published tools that are able to obtain a minimal equivalent logic program. In this paper we present the first version of a tool called that is able to efficiently obtain minimal and equivalent representations for any logic program in Here-and-There. The described tool uses an hybrid method both leveraging a modified version of the Quine-McCluskey algorithm and Answer Set Programming techniques to minimize fairly complex logic programs in a reduced time.

Highlights

  • In the field of logic programming it has always been f great importance to reduce the formulae and expressions to their minimal conjunctive or disjunctive normal forms (CNF and DNF respectively), as this reduces the number of logic OR and AND gates needed to implement the function as a circuit

  • In this paper we describe a first approach to a tool that is able to minimize logic programs and theories in Here-and-There logic leveraging both the Quine-McCluskey algorithm alongside the power of Answer Set Programming

  • We have developed a novel tool that implements the modified version of Quine-McCluskey’s method for HT, while using the capabilities of Answer Set Programming to perform the minimal coverage of the initial countermodels, as well as using it to test and validate the results

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Summary

Introduction

In the field of logic programming it has always been f great importance to reduce the formulae and expressions to their minimal conjunctive or disjunctive normal forms (CNF and DNF respectively), as this reduces the number of logic OR and AND gates needed to implement the function as a circuit. This topic has been broadly studied for Boolean Logic and well known methods such as the Karnaugh Maps [1] and Quine-McCluskey algorithm [2,3] have served as base for powerful tools such as ESPRESSO [4] and BOOM [5].

Materials and Methods
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