[Paper Review] Tuning Fuzzy Logic Programs with Symbolic Execution

Ginés Moreno, Jaime Penabad+1 more|arXiv (Cornell University)|Aug 16, 2016

Logic, Reasoning, and Knowledge24 references3 citations

TL;DR

This paper introduces symbolic multi-adjoint logic programming (sMALP), a framework that allows fuzzy logic programs to include symbolic truth degrees and connectives, enabling automated tuning via symbolic execution. By delaying evaluation of unknown parameters and using test cases, the method automatically computes optimal weights and connectives, significantly reducing manual trial-and-error in program configuration.

ABSTRACT

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well as the most appropriate fuzzy connectives and operators. In this paper, we introduce a symbolic extension of fuzzy logic programs in which some of these parameters can be left unknown, so that the user can easily see the impact of their possible values. Furthermore, given a number of test cases, the most appropriate values for these parameters can be automatically computed.

Motivation & Objective

• Address the challenge of manually selecting appropriate truth degrees and fuzzy connectives in multi-adjoint logic programming (MALP), which is time-consuming and error-prone.
• Enable users to specify fuzzy logic programs with symbolic parameters (unknown truth degrees and connectives) to explore their impact before final configuration.
• Develop an automated tuning process that computes optimal parameter values based on a set of user-provided test cases.
• Integrate the proposed framework into the FLOPER system for practical deployment and extension with optimization techniques.
• Provide a formal symbolic operational semantics that ensures correctness by preserving equivalence between symbolic and concrete evaluations.

Proposed method

• Extend MALP syntax to support symbolic truth degrees and symbolic connectives (e.g., unknown adjoint pairs like $\langle\&_{\mathtt{P}}, \leftarrow_{\mathtt{P}}\rangle$) in program rules.
• Define a symbolic operational semantics that delays evaluation of symbolic expressions, producing symbolic computed answers containing unresolved parameters.
• Prove correctness of the symbolic semantics by showing that symbolic evaluation followed by instantiation yields the same result as concrete evaluation after parameter substitution.
• Formulate the tuning process as a constraint satisfaction problem: given test cases, compute parameter values that minimize deviation from expected truth degrees.
• Use the FLOPER system as a target platform for compiling and executing sMALP programs, leveraging its existing support for derivation trees and declarative tracing.
• Explore integration with fuzzy SAT/SMT solvers in future work to improve scalability and efficiency of the tuning process.

Experimental results

Research questions

• RQ1 How can fuzzy logic programs be extended to support symbolic truth degrees and connectives while preserving semantic correctness?
• RQ2 Can symbolic execution in fuzzy logic programming enable automated tuning of parameters without requiring manual trial-and-error?
• RQ3 What is the formal relationship between symbolic evaluation and concrete evaluation in fuzzy logic programs with unknown parameters?
• RQ4 How effective is the proposed tuning method in achieving desired outputs across multiple test cases compared to manual configuration?
• RQ5 What are the prospects for integrating symbolic tuning with existing fuzzy logic solvers and verification tools?

Key findings

• The symbolic operational semantics correctly preserves the outcome of concrete evaluation when symbolic parameters are instantiated, ensuring soundness of the approach.
• The framework enables users to explore the impact of different truth degrees and connectives (e.g., Łukasiewicz, Gödel, product logic) on program behavior before final configuration.
• The tuning process successfully computes optimal parameter values for a set of test cases, reducing the need for iterative manual refinement.
• The method has been formally proven correct and is designed for integration into the FLOPER system, which supports compilation, execution, and trace generation for MALP programs.
• Preliminary results suggest that symbolic tuning can be combined with fuzzy SAT/SMT solvers to improve scalability and efficiency in large-scale parameter configuration.
• The approach supports complex configurations involving multiple symbolic connectives and truth degrees, as demonstrated in the evaluation with diverse test cases and parameter combinations.