In the field of thought, where concepts exist,
A method of reasoning persists,
Examining statements, to determine truth,
An area of study, with systematic proof.
The philosophy of logic, a subject of study,
Investigates foundations, methodically,
It analyzes principles, of correct inference,
In theory and practice, with adherence.
Types of logic, classified and listed:
Formal, metalogic, classical enlisted,
Extended and non-standard, complete the set,
A structure for reasoning, commonly met.
Modus ponens, an inferential rule,
Links premises to conclusions, a cognitive tool,
If P implies Q, and P is true,
Then Q is inferred, logically due.
Researchers of logic, across time periods,
Added to the field, expanding its horizons,
From earlier eras to current times,
They've enhanced the subject in numerous lines.
Non-contradiction law, a logical base,
States contradictions cannot share time and space,
A statement and its negation, mutually incompatible,
In identical contexts, this rule is applicable.
De Morgan's laws, logical equations,
Connect conjunctions, disjunctions in relations,
Negating a conjunction, equals negations disjoined,
And conversely, these rules are conjoined.
In this area of reason, we examine,
Through logical structures, we determine,
The philosophy of logic, a field extensive,
Progressing our knowledge, comprehensive.