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A Computationally Grounded Framework for Cognitive Attitudes
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Introduces a modal logic of cognitive attitudes (implicit belief, complete/realistic attraction and repulsion) with a succinct belief-base semantics, an axiomatization, a dynamic extension, and a PSPACE model checker via TQBF.
Problem
Kripke-style semantics for logics combining epistemic and motivational attitudes are not succinct, making model checking infeasible for realistic multi-agent scenarios.
Approach
Defines epistemic, attraction and repulsion accessibility relations directly from agents' explicit belief bases (with good/bad atoms encoding desires), yielding a succinct computationally grounded semantics for cognitive attitudes, with modal operators for complete and realistic attraction/repulsion and dynamic belief expansion/forgetting.
Key results
- Axiomatization LCA is proven sound and complete for the class of models M.
- Model checking for the dynamic language is PSPACE-complete, via a poly-time reduction to TQBF.
- Implemented Haskell/BDD model checker checks Example 1 with 60 children (|S_Γ| ≈ 2^1080) in 5.67 seconds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase the number of agents from 1 to 60 | Symbolic model checker on Example 1 · Example 1 | execution time (sec.): 0.07 -> 5.67 | Hurt |
Surprising findings
- The five modal operators are not mutually expressible (Theorem 1), so complete and realistic attraction/repulsion are independent primitives.
- The state space can be astronomically large (|S_Γ| up to 2^1080) yet model checking remains feasible in seconds for the example.
Limitations
- Belief expansion can make belief bases inconsistent; belief revision is only treated in the extended version.
- Experiments cover only a single concrete example and only the static fragment of the language.
- Preference is defined qualitatively; graded motivation and strong motivation are left to future work.
Experimental setup
Benchmarks: mother-child speech act example (Example 1) scaled to up to 60 agents
Metrics: execution time (sec.) number of states |S_Γ|
Baselines: Kripke model semantics
Builds on: Kripke semantics belief base semantics (Lorini 2018, 2020) dynamic logic window modality Konolige belief base
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