1
vote
2answers
75 views

How to deal with equivalences in proofs?

There is a part I need clarification on regarding the use of equivalence and its symmetry. From what I understand in regards to symmetry is that: $ (p \equiv q) \equiv (q \equiv p) $. Given p and q ...
5
votes
3answers
329 views

Derive by modus ponens $[A\rightarrow(B\rightarrow C)]\rightarrow[(A\rightarrow B)\rightarrow(A\rightarrow C)]$

How could I derive by modus ponens the formula $$[A\rightarrow(B\rightarrow C)]\rightarrow[(A\rightarrow B)\rightarrow(A\rightarrow C)]$$ from, and just from, the following axiom schemata? $(A\lor ...
3
votes
1answer
147 views

Axioms based on $\leftrightarrow, \lor, \bot$ for propositional intuitionistic logic?

Propositional intuitionistic logic can be axiomatized based on $\;\to, \land, \lor, \bot\;$, with modus ponens $$ \text{from }\; \phi \;\text{ and }\; \phi \to \psi \;\text{ infer }\; \psi $$ as the ...
2
votes
1answer
236 views

Axioms and deduction rules of Propositional Calculus

I'm looking for a list of axioms and fundamental deduction rules of Propositional Calculus.
7
votes
6answers
1k views

How to demystify the axioms of propositional logic?

How might I go about getting some intuition on the typical axiom schemes given for propositional logic? They seem rather mysterious at first glance. For example, these are taken from: ...
3
votes
3answers
429 views

Why is axiomatic system needed in propositional logic?

I am trying to learn propositional logic. I have read that axiomatic system is defined since there are some problems which can not be solved using truth tables. I have found such a problem in ...
11
votes
3answers
654 views

In axiomatization of propositional logic, why can uniform substitution be applied only to axioms?

I'm reading an introductory book about mathematical logic for Computation (just for reference, the book is "Lógica para Computação", by Corrêa da Silva, Finger & Melo), and would like to ask a ...