modus ponens वाक्य

One of the first and most successful compromises was to develop languages based predominately on modus ponens, i . e . IF-THEN rules.
Can I describe modus ponens as an algebraic operation in this structure ?-talk [ + ] 06 : 10, 12 June 2006 ( UTC)
It can be shown that with only these three axiom schemata and " modus ponens ", one can prove all tautologies of the propositional calculus.
Also, from the first element of, last element, as well as modus ponens, is a consequence, and so R \ in \ Gamma.
On the other hand, DT is so useful for simplifying the syntactical proof process that it can be considered and used as another inference rule, accompanying modus ponens.

Here, because of the simple syntax of pure Prolog programs, " implied by " can be understood very simply as derivability using modus ponens and universal instantiation alone.
We describe here a Hilbert system with nine axioms and just the rule modus ponens, which we call the one-rule axiomatisation and which describes classical equational logic.
Most axiomatic systems have only the rule of modus ponens ( and sometimes substitution ), so it requires only verifying the validity of the axioms and one rule of inference.
However, if a formal system is introduced where modus ponens is simply a rule of inference defined by the system, then it can be abided by simply because it is so.
Enderton, for example, observes that " modus ponens can produce shorter formulas from longer ones ", and Russell observes that " the process of the inference cannot be reduced to symbols.