The calculus can be axiomatized with the formulas:
Calcolo geometrico (1888; “Geometric Calculus”) contains his first work on mathematical logic.
Peirce then describes a decision procedure for the calculus:
Gödel adds the following rules and axioms to the propositional calculus.
Consider next the homomorphic mapping from the syntactic source calculus to the semantic target calculus.
PDL is in fact a generalization of Hoare calculus in the sense that all the rules of the Hoare calculus can be proven in the axiomatic system of PDL.
If one builds one's deductive calculus with care, one will be able to convince oneself that all the formulae derivable in the calculus are logical truths.
To this end we will explain the event calculus, which is an extension of McCarthy’s situation calculus (McCarthy 1977) developed by Kowalski and Sergot (1986).
The implementation of a calculus invariably involves making some modifications to the calculus and this results, strictly speaking, in a new calculus.
…formal system differs from a logical calculus in that the system usually has an intended interpretation, whereas the logical calculus deliberately leaves the possible interpretations open.
When proof-objects are added to the natural deduction calculus it becomes a typed lambda calculus with dependent types, which extends Church’s original typed lambda calculus.
Turing introduced his thesis in the course of arguing that the Entscheidungsproblem, or decision problem, for the functional calculus—also known as the first-order predicate calculus—is unsolvable.
Kleene had taken up Ketonen's calculus from the Bernays' review and also treated intuitionistic sequent calculus in which invertibility is more restricted than in the classical calculus.
This led to the Coq system, which is based on the calculus of inductive constructions (Paulin-Mohring 1993), a theory which extends the calculus of construction with primitive inductive types and families.
The rest of the deductions in the full polyadic predicate calculus, as well as all of those in the monadic predicate calculus and propositional calculus, measure 0, (see Sequoiah-Grayson 2008).
The event calculus (Kowalski and Sergot 1986, Shanahan 1990, Shanahan 1995) and fluent calculus (Thielscher 2005) are alternatives to the situation-based representation of actions in the situation calculus.
Calculus, branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).
He begins with the propositional calculus, then moves to monadic quantificational logic (with an extended discussion of the calculus of classes, and of the Aristotelian syllogism), and then to the “function calculus”.
The second epsilon theorem shows that any detour through the epsilon calculus used to derive a theorem in the language of the predicate calculus from axioms in the language of the predicate calculus can also be avoided.
Both men used coordinates to develop notations that expressed the ideas of calculus in full generality and led naturally to differentiation rules and the fundamental theorem of calculus (connecting differential and integral calculus).
calculus
noun object
- a hard lump produced by the concretion of mineral salts; found in hollow organs or ducts of the body
noun object
- an incrustation that forms on the teeth and gums
noun cognition
- the branch of mathematics that is concerned with limits and with the differentiation and integration of functions
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