Automata, Model Checking & Formal Semantics

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Abstractions about automata, temporal logic, model checking, formal grammars, computation, quantifier complexity, rule-based inference, and interpretability between systems.

10 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Cointerpretability — Compare formal theories by a logic-preserving translation in the reverse language direction that reflects the translated theory's theorems, a dual of interpretability tied to Σ₁-conservativity for suitable arithmetical theories.
• Computation Tree Logic — A branching-time temporal logic whose formulas pair universal or existential path quantification with next, eventually, always, or until modalities over Kripke structures.
• DATR — A declarative node–path–value equation language for compact lexical knowledge bases with default inheritance, override, path extension, and query evaluation.
• Deterministic Finite Automaton — Recognize a regular language by starting in one of finitely many states, taking exactly one transition for each input symbol, and accepting according to the unique terminal state.
• Formula Game — Evaluate a closed quantified Boolean formula as a perfect-information contest in which Existential and Universal assign their variables in prefix order and truth is equivalent to Existential having a winning strategy.
• Model Checking — Verify a system by taking a finite-state model plus a temporal-logic property and exhaustively exploring every reachable state to decide whether the property holds universally, returning a concrete counterexample trace on failure.
• Negation as Failure — Treat a ground goal's finite, exhaustive proof failure under a declared logic program and search semantics as defeasible support for weak default negation, while preserving nonmonotonicity, nontermination, floundering, and classical-negation boundaries.
• Quantifier Rank — Assign a logical formula the maximum nesting depth of its quantifiers, stratifying expressibility so bounded-rank formulas, types, and structure-distinguishing games can be compared at a fixed logical depth.
• Regular Grammar — A regular grammar is a formal grammar whose productions keep at most one nonterminal consistently at one edge of the right-hand side, so derivation carries only finite-state memory and generates exactly a regular language under the declared right- or left-linear convention.
• Turing Machine — The canonical formal model of computation — finite control plus an unbounded read-write tape governed by a finite transition function — whose one unbounded resource is the tape, and against which computability and complexity are given exact, provable meaning.