Formal Declarative Proposition

A Formal Declarative Proposition is a logic proposition that is mapped to a truth value.

• AKA: Truthbearer, Closed Logic Formula, Logic Statement.
• Context:
  • It can (typically) abide by a Logic Theory (e.g. be a propositional logic formula or a first-order formula).
  • It can range from being a False Claim to being a True Claim.
  • It can range from being a Well-Formed Declarative Proposition to being a Non-Well-Formed Declarative Proposition.
  • It can be a part of:
    • a Logic Argument (of a claim).
    • a Logic Conclusion.
  • It can (often) have Meaning (relate to the real world, e.g. a counter-factual proposition).
• Example(s):
  • an Axiom.
  • a Conditional Rule that ...
  • "I have seen a white swan. ⇒ True
  • "I have never seen a black swan. ⇒ True
  • Socrates was a man ⇒ True
  • A triangle has three sides ⇒ True
  • Paris is the capital of England ⇒ False
  • If [math]\displaystyle{ p }[/math] then q. (a Production Rule).
  • “Hesperus ≠ Phosphorus ⇒ True” (see Frege).
  • a Horn Clause.
  • a Production Rule.
  • an Evidence Statement (a Justifier).
  • a Premise. (e.g. a Belief).
  • …
• Counter-Example(s):
  • Socrates was a man (a logic expression without a truth value assignment).
  • "Person X will likely choose Y with 85% likelihood". (a probabilistic statement).
  • "Who are you?" (a Query).
  • a Linguistic Sentence.
  • a Command, such as “Run!”
  • “Greeness perambulates”
  • “I had one grunch but the eggplant over there."
• See: Declarative Sentence, Utterance, Rule Antecedent, Rule Consequent, Formulation (Logic).

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References

2017

• (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/statement_(logic) Retrieved:2017-1-19.
  • In logic, a statement is either (a) a meaningful declarative sentence that is either true or false, or (b) that which a true or false declarative sentence asserts. In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement.

2012

• http://www.ontotext.com/factforge/logical-statement
  • Logical statement is a declarative sentence that is either true or false. A statement differs from a sentence in that a sentence is only one formulation of a statement. There may be many sentences expressing the same statement.

2010

• (Wikipedia, 2010) ⇒ http://en.wikipedia.org/wiki/Statement_(logic)
  • In logic a statement is either (a) a meaningful declarative sentence that is either true or false, or (b) that which a true or false declarative sentence asserts. In the latter case, a statement is distinct from a sentence in that a sentence is only one formulation of a statement, whereas there may be many other formulations expressing the same statement.

    Philosopher of language, Peter Strawson advocated the use of the term "statement" in sense (b) in preference to proposition. Strawson used the term "Statement" to make the point that two declarative sentences can make the same statement if they say the same thing in different ways. Thus in the usage advocated by Strawson, "All men are mortal." and "Every man is mortal." are two different sentences that make the same statement.

    In either case a statement is viewed as a truth bearer.

    Examples of sentences that are (or make) statements:

    • "Socrates is a man."
    • "A triangle has three sides."
    • "Madrid is the capital of Spain."

2009

• (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=statement
  • S: (n) affirmation, assertion, statement (the act of affirming or asserting or stating something)
  • …
• http://www.uky.edu/~rosdatte/phi120/glossary.htm
  • statement: A statement is a sentence that is either true or false, such as "The cat is on the mat." Many sentences are not statements, such as "Close the door, please", "How old are you?"
• CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
  • formula: A formula is a sentential expression in a formal language. If the expression is closed (that is, if it has no unbound variables) it can be used to express something about the world. Closed formulas are analogous to declarative sentences in English. In CycL, formulas that are well-formed are called "CycL formulas". For more information about the syntax of CycL formulas, click here.
• http://www.sparknotes.com/testprep/books/sat2/math2c/chapter12section1.rhtml
  • A logic statement is written in the form “If p, then q,” where p and q are events. “If p, then q” can also be written as, and it states that if event p occurs, then event q will also occur.

Every “If p, then q” statement has an equivalent statement; this second statement is known as the contrapositive, which is always true. The contrapositive of “If p, then q” is “If not q, then not p.” In symbols, the contrapositive of is (here, the symbol ~ means “not”). To formulate the contrapositive of any logic statement, you must change the original statement in two ways.

• • • 1. Switch the order of the two parts of the statement. For example, “If p, then q” becomes “If q, then p.”
    • 2. Negate each part of the statement. “If q, then p” becomes “If not q, then not p.”

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