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Social, Legal, Ethical, Empathetic, and Cultural Rules: Compilation and Reasoning
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Translates SLEEC (social, legal, ethical, empathetic, cultural) normative rules into classical propositional logic via a formal 'unless ... in which case' semantics, analyses reasoning complexity, and shows implementation in ASP and Prolog.
Problem
SLEEC rules elicited in natural language for AI and autonomous systems need systematic translation into a machine-interpretable formal language supporting automated reasoning.
Approach
A linguistic analysis of the SLEEC rule pattern justifies defining 'unless' as a material implication (¬ψ→ϕ) and 'unless ... in which case' as a conjunction, yielding a quadratic-size classical logic compilation; reasoning is then done with SAT solvers, ASP, or Prolog.
Key results
- Proves that entailment of an obligation from SLEEC rules is coNP-complete even when conditions and obligations are literals, via reduction from 3SAT.
- Shows entailment is in PTIME when all conditions are negative literals and all obligations positive literals, by reduction to HORNSAT.
- Shows the compiled form of a SLEEC rule has size quadratic in the original rule size (|compile(σ)| = O(|σ|^2)).
Surprising findings
- 'Unless' is not equivalent to exclusive-or; the converse implication is only a Gricean conversational implicature, not part of the meaning.
Limitations
- Worst-case reasoning is coNP-hard unless restricted to Horn-like forms.
- Ethical review of the overall system remains essential beyond the formal implementation.
- Demonstrated on a single running example (nursing home curtain rule).
Experimental setup
Baselines: SLEECVAL normative multi-agent formalisms (Meyer and Wieringa 1994; Gabbay et al. 2013, 2
Builds on: SLEEC rule elicitation methodology (Townsend et al. 2022) Quine's logical reading of unless SLEECVAL (Yaman et al. 2023)
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