The phrase "arithmetical logic" is correct and usable in written English.
It can be used in contexts discussing mathematical reasoning, logical operations, or the foundations of mathematics.
Example: "In the study of arithmetical logic, we explore the principles that govern numerical reasoning and proof."
Alternatives: "mathematical logic" or "numerical logic".
4.5 Bounded arithmetic Another connection between logic and computational complexity is provided by first-order arithmetical theories which are similar in form to familiar systems such as Primitive Recursive Arithmetic and Peano arithmetic.
The central problem was thus to justify the use of classical logic in mathematical proofs, arithmetical ones in the first place.
The above result by De Jongh et al. shows a strong feature of provability logic: for many different arithmetical theories, GL captures exactly what those theories say about their own provability predicates.
The system employs a novel, dual-leveled language that follows fuzzy logic by interpreting the logical or and and as the arithmetical max and min. Numerous properties of Σ, illustrating its intuitive appeal for the intended purpose, are derived.
In the Ambigua, a broad range of theological topics cosmology, anthropology, the philosophy of mind and language, allegory, asceticism, and metaphysics—are transformed in a synthesis of Aristotelian logic, Platonic metaphysics, Stoic psychology, and the arithmetical philosophy of a revived Pythagoreanism.
Gödel numbering provides a quantifier-free formula G x) which (numeralwise) expresses the predicate "x is the code of a proof in HA of (0 = 1)." By intuitionistic logic with the decidability of quantifier-free arithmetical formulas, HA proves ∀x ∃yG y) ∨ ¬G x)).
Tri-state logic (¯1,0,1) plays a significant role in carry free arithmetical operation.
In this paper, we study the differences between Fast and TReX acceleration techniques and show that although Fast remains in Presburger logics while accelerating, TReX can produce 1st order arithmetical formulas even when accelerating functions.
If one accepts a certain open-endedness of the collection of arithmetical predicates, then a categoricity theorem of sorts for arithmetic can be obtained without overstepping the bounds of first-order logic and without appealing to an informal concept of computability.
Provability logic is a modal logic that is used to investigate what arithmetical theories can express in a restricted language about their provability predicates.
