Term
|
Definition
| Ls is complete if and only if, for every set of sentences, Γ, and any sentence, Φ, if Γ |= Φ, then Γ |- Φ |
|
|
Term
|
Definition
| A sentence, p, is contingent if and only if there is at least one model of p and at least one interpretation that is not a model of p )this is, p is true under some interpretations, and false under others). |
|
|
Term
|
Definition
| A sentence, p, is contradictory if and only if p has no model (that is. p is false under every interpretation). |
|
|
Term
|
Definition
| An interpretation, I, is a model of a sentence, p, if and only if I(p) is true. If Γ is a set of sentences, then I is a model of Γ if and only if every sentence in Γ is true under I. |
|
|
Term
|
Definition
| A sentence, p, is logically true if and only if every interpretation is a model of p (that is, p is true under every interpretation). |
|
|
Term
|
Definition
| A language in which the discussion of some object language is conducted. |
|
|
Term
|
Definition
| A language under discussion |
|
|
Term
|
Definition
| |= . A set of sentences, Γ logically implies a sentence,Φ ,(Γ |= Φ ) if and only if Φ cannot be false if Γ (i.e., every sentence in Γ) is true. |
|
|
Term
|
Definition
1. Every member of Cs (a sentential constant) is a sentence of Ls;
2. If p is a sentence of Ls, then ¬p is a sentence of Ls;
3. If p and q are sentences of Ls, then (p˄q) is a sentence of Ls;
4. If p and q are sentences of Ls, then (p˅q) is a sentence of Ls;
5. If p and q are sentences of Ls, then (pͻq) is a sentence of Ls;
6. If p and q are sentences of Ls, then (pΞq) is a sentence of Ls;
7. Nothing is a sentence of Ls that is not constructed in accord with rules 1-6. |
|
|
Term
|
Definition
| An interpretation, I, of Ls is an assignment to each member of Cs (that is, to each atomic sentence) one and only one of the truth values {true, false} and an assignment to the members of Cc (that is, to the connectives) the truth functional meanings. |
|
|
Term
| Truth-Functional Language |
|
Definition
| A language in which the truth value of every sentence in Ls is a function of the truth values of its constituent sentences. |
|
|
Term
|
Definition
| When Γ logically implies Φ, then Φ is said to be a logical consequence of Γ. |
|
|
Term
| Validity (Valid Sentence in Ls) |
|
Definition
| If p and q make up a sentence in which p is a premise and q is the conclusion, then when p logically implies q, the sentence is valid. |
|
|
Term
|
Definition
| Ls is sound if and only if, for every set of sentences, Γ , and any sentence, Φ, if Γ deductively yields Φ (Γ |-Φ), then Γ logically implies Φ (Γ |= Φ). |
|
|
Term
|
Definition
| When people make estimates by starting from an initial value that is adjusted to yield the final answer. The adjustment is typically insufficient. I.E. How many countries in the UN example. |
|
|
Term
|
Definition
| Situations where people asses the frequency of a class or the or the probability of an event by the ease with which instances or occurrences can be brought to mind. |
|
|
Term
|
Definition
| Lp is complete, just in case, if a sequence is valid, a derivation can be given for it in Lp: if Γ |= Φ, then Γ |- Φ. |
|
|
Term
|
Definition
| Lp is sound, just in case every derivation expressible in Lp is valid: Where <Γ,Φ> is a sequence, if Γ |- Φ, then Γ |= Φ. |
|
|
Term
|
Definition
| When we reason deductively, the truth of our premises guarantees the truth of our conclusion. |
|
|
Term
|
Definition
| When we reason inductively, our premises provide only probabilistic support for our conclusion. |
|
|
Term
| Domain / Universe of Discourse |
|
Definition
| The set of individuals over which the variable in a sentence range.The domain of discourse, unless otherwise specified, is unrestricted; it includes every object. |
|
|
Term
|
Definition
| A sequence is invalid if there is an interpretation, any interpretation, under which its premises are true and its conclusion false. |
|
|
Term
|
Definition
| Two sentences are logically equivalent if they have identical truth conditions. |
|
|
Term
|
Definition
| Principles which reduce the complex task of assessing probabilities and predicting values to simpler judgmental operations. |
|
|
Term
|
Definition
| A heuristic in which probabilities are evaluated by the degree to which A is representative of B, that is, by the degree to which A resembles B. I.E. Engineers and Lawyers example. |
|
|
Term
|
Definition
| A disjunction effect occurs when people prefer x over y when they know that event A obtains, and they also prefer x over y when they know that event A does not obtain, but they prefer y over x when it is unknown whether or not A obtains. |
|
|
Term
|
Definition
| Two events in conjunction are less likely to occur than each event separately. I.E. Feminist bank teller example. |
|
|
