Stephen Toulmin, originally a British logician, is now a professor at USC. He became
frustrated with the inability of formal logic to explain everyday arguments, which
prompted him to develop his own model of practical reasoning.
The first triad of his model consists of three basic elements:

A claim is the point an arguer is trying to make. The claim is the
proposition or assertion an arguer wants another to accept.
The claim answers the question, "So what is your point?"
example: "You should send a birthday card to Mimi, because she sent you one on
your birthday."
example: "I drove last time, so this time it is your turn to drive."
There are three basic types of claims:
fact: claims which focus on empirically verifiable phenomena
judgment/value: claims involving opinions, attitudes, and subjective
evaluations of things
policy: claims advocating courses of action that should be undertaken
Grounds refers to the proof or evidence an arguer offers.
Grounds answers the questions, "What is your proof?" or "How come?" or
"Why?"
Grounds can consist of statistics, quotations, reports, findings, physical evidence, or
various forms of reasoning.
example: "It looks like rain. The barometer is falling."
example: "The other Howard Johnson's restaurants I've been in had clean restrooms,
so I'll bet this one has clean restrooms too."
grounds can be based on:
evidence: facts, statistics, reports, or physical proof,
source credibility: authorities, experts, celebrity endorsers, a close friend, or
someone's say-so
analysis and reasoning: reasons may be offered as proof
The warrant is the inferential leap that connects the claim with the
grounds.
The warrant is typically implicit (unstated) and requires the listener to
recognize the underlying reasoning that makes sense of the claim in light of the grounds.
The warrant performs a "linking" function by establishing a mental connection
between the grounds and the claim
example: "Muffin is running a temperature. I'll bet she has an infection." warrant:
sign reasoning; a fever is a reliable sign of an infection
example: "That dog is probably friendly. It is a Golden Retriever." warrant:
generalization; most or all Golden Retrievers are friendly
warrants can be based on:
ethos: source credibility, authority
logos: reason-giving, induction, deduction
pathos: emotional or motivational appeals
shared values: free speech, right to know, fairness, etc.
note: these categories aren't mutually exclusive, there is considerable overlap among
the three
The second triad of the Toulmin model involves three addditional
elements:
Backing provides additional justification for the warrant.
Backing usually consists of evidence to support the type of reasoning employed by the
warrant.
The qualifier states the degree of force or probability to be attached
to the claim.
The qualifier states how sure the arguer is about his/her claim
The rebuttal acknowledges exceptions or limitations to the argument.
The rebuttal admits to those circumstances or situations where the argument would not
hold.