Fuzzy grammars and weighted automata usually attach to each word a single grade, which records how strongly the word is generated but not how far that record can be trusted. We study weighted grammars and finite automata whose weights are scalar grade-reliability pairs inspired by Z-numbers. Sequential composition multiplies both components, while aggregation selects a derivation by its credible grade, the product of grade and reliability, with ties resolved by grade. On the canonical carrier, in which the weights of zero grade or zero reliability are identified with zero, the resulting structure is a commutative selective semiring, isomorphic to a subsemiring of a lexicographically ordered product, and its credible-grade projection is a homomorphism onto the Viterbi semiring. We compare several alternative combination rules and identify the carriers on which the relevant algebraic laws hold. Standard results on weighted automata then yield a rational characterization and closure properties. We prove that positive credible-grade cuts and selected-run reliability filters of finite automata are regular and effectively constructible for rational weights and thresholds, and we exhibit distinctions that the scalar projection cannot see: a reliability filter that no scalar reweighting of the same one-state automaton implements, nonmonotonicity under the addition of runs, and an unambiguous automaton with no deterministic equivalent although its scalar projection is deterministic. A count-based example illustrates an attestation penalty for grammar rules. The construction concerns scalar pairs, and its extension to arbitrary fuzzy-valued Z-numbers remains open.
A rule written for people fixes its atomic conditions and connectives but leaves open how the connectives are bracketed, and each bracketing is a different logical reading that an autoformalizer must resolve or expose. We study the scope grammar, a deliberately ambiguous context-free grammar whose derivation trees are the readings of a connective skeleton and whose quotient by logical equivalence is what matters downstream. A skeleton with $k$ binary connectives has $C_k$ derivation trees, the $k$-th Catalan number, but far fewer logically distinct readings. For the positive, repetition-free fragment we make the gap exact: through the uniqueness of the read-once normal form we characterize the realizable normal forms by lowest common ancestors and count them with a two-label recurrence over the operator word, verified against exhaustive enumeration up to eleven atoms. The count is invariant under reversal and $\wedge/\vee$ duality; a skeleton is ambiguous if and only if it uses both $\wedge$ and $\vee$, a one-pass test; and the number of classes is at least $2^{\lfloor n/3\rfloor}$. Up to fifteen atoms the alternating pattern is the worst case; its count has a cubic generating function, is the 3-Schröder sequence (OEIS A137842), and grows with base $\varphi^{5/2}\approx3.330$, below the Catalan base 4. We reduce maximality to an inequality on increments, verified to sixteen atoms, and explain why local exchange arguments cannot prove it. We also treat negation, exceptions, and background axioms, where normal-form uniqueness still decides equivalence but counting is open.