Reasoning with Constraints: Decision Procedures, Witnesses and Applications
Bibliographic record
Abstract
Logic, and constraint satisfiability are key ingredients in automated reasoning for solving real-world software engineering problems. A wide range of reasoning tasks such as model checking, verification, and synthesis can be encoded as constraint satisfaction problems in a suitable logic and solved with algorithms that efficiently decide their satisfiability. To enable the satisfiability-based approach to reason about a problem, some key questions need to be addressed: (1) What is a suitable logic to model the essence of the problem and how to decide its satisfiability? (2) How to trust correctness of the satisfiability result and explain its cause? and (3) How to encode reasoning tasks of interest as satisfiability problems in the logic? In this thesis, we investigate these questions, considering subsets of first-order logic and addressing problems of different complexities. First, we study the problem of reasoning about infinite state systems through the lens of a variance of FOL, first-order logic with quantifier over relational objects (FOL*). The logic introduces a novel concept: relational objects, to capture system operations of unbounded sizes with time and data from unbounded domains. We develop an efficient semi-decision procedure for FOL* satisfiability with incremental approximations. We also extend FOL* to support aggregation functions over relational objects to enable the specification and efficient reasoning about global properties. Next, we address the question of validating the correctness of satisfiability results. We propose approaches to support the proof of unsatisfiability (UNSAT) for FOL* and finite-domain monotonic theories (SMMT). To efficiently and soundly verify the unsatisfiability of FOL* and SMMT formulas, we formalize the theory semantics as a set of derivation rules and capture the reasoning towards unsatisfiability as derivation sequences. The correctness of the derivation can be verified on the premise that each derivation step can be efficiently checked against the derivation rules. By checking the UNSAT proof, we can establish a correctness guarantee for the unsatisfiability result and diagnose the causes of unsatisfiability. Then, we apply FOL* satisfiability to automatically reason about normative requirements written in domain-specific languages. We capture the semantics of requirements in FOL* and encode the tasks of checking the well-formedness properties into FOL* queries. We use the FOL* satisfiability result, including the satisfying solution, and UNSAT diagnosis to provide user-friendly diagnostics to pinpoint the causes of well-formedness issues. Finally, we conclude this thesis by discussing the limitations and future works.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.006 | 0.019 |
| Open science | 0.003 | 0.006 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".