I'm going attempt rolling Bumble's and Hypnosofil's responses into something and add a dash of background
NB: This has been challenged as a mischaracterization. See the comments below.
Yes and no. One way logic can be dichotomized is between the formal and informal, and the answer to your question depends on the types of logic you choose. Perhaps the most salient example to show the difference is between the material and indicative conditional which highlights the difference between natural and artificial languages.
The traditional disputes of philosophers are, for the most part, as unwarranted as they are unfruitful. The surest way to end them is to establish beyond question what should be the purpose and method of a philosophical enquiry. - A. J. Ayer
You have highlighted an important and often unnoticed phenomenon in logic, and that is the distinction between how the human reason actually works, and how we can model and mechanize human reason. Since the 1950's when AI researchers attempted to begin attacking the problem of how can we solve problems using reason and common sense, they brushed up a scientific fact that human reason is defeasible and does not use formal languages. Let's look at the difference:
Technically, introductory formal logic uses the material conditional which is actually a mathematical mapping, technically a 2-variable relation whose domain (T,F) is logically equivalent to the codomain value of T. Since each distinct ordered pair in the domain maps to an element, it's a function in the technical sense. It would have to be one-to-one to be injective and is not. See the mapping:
p q p → q
T T T
T F F
F T T
F F T
WHAT THE HECK DID YOU SAY? Odds are if you're not a mathematician, something similar ran through your mind. There's a strange middle ground where some thinkers know enough math to not know this isn't actually how people think, and this is a classic motif in the criticism of philosophy, that philosophers are a little too detached from reality even when they study ontology. Let's try that again for the non-formalists among us using natural language.
"If the accused man committed the murder, he had an accomplice." This is the natural language or indicative use of conditional. Note maybe the statement 'He committed the murder' is false and is counterfactual. What does the law say about the difference between murder and homicide? If we don't have persuasive evidence such as a videotape of the act and are forced to rely on (legal) testimony, how should we decide what to decide? Even if we saw the act, is mens rea present?
Notice the difference in the approach to problem-solving? The first is formal logic and deductively valid, and the second is informal logic and cogent. In philosophy, this distinction was drawn on and the overuse of technical definitions and abstractions such as formal logic was criticized by the ordinary language philosophers who appeal to intuition much more strongly.
Perhaps the most intriguing biography is that of Ludwig Wittgenstein who is characterized as having an early and later phase and embodying both. In fact, his thoughts about family resemblance were extremely influential in meta-ontological thinking. Another important figure is Stephen Toulmin whose model of argumentation in Uses of Argument seems to be practically ignored by those in computational fields like mathematics and computer science. (I speak from direct experience on both fronts).