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22 Cards in this Set
- Front
- Back
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Atomic Sentence
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The most basic sentences of FOL, those formed by a predicate followed by the right number of names (or complex terms, if the language contains function symbols). Atomic sentences in FOL correspond to the simplest sentences in English.
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Arity of a Predicate
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Indicates the number of arguments (in the second sense of the word) it takes. A predicate with arity of one is called unary. A predicate with an arity of two is called binary. It's possible for a predicate to have any arity, so we can talk about 6-ary or even 113-ary predicates.
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Truth-Functional Connective
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A sentence connective with the property that the truth value of the newly formed sentence is determined soley by the truth value(s) of the constituent sentences(s), nothing more. Examples are the Boolean connectives (¬,∧,∨) and the material conditional and biconditional (⟶,↔).
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Formal Proof vs. Informal Proof
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A proof is a step-by-step demostration that one statement (the conclusion) follows logically from some others (the premises). A formal proof is a proof given in a formal system of deduction (Fitch format), whereas an informal proof is generally given in English, without the benefit of a formal system (sentence format).
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Logical Consequence
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A sentence S is a logical consequence of a set of premises if it is impossible for the premises all to be true while the conclusion S is false.
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Scope of a connective
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The scope of a quantifier in a wff is that part of the wff that falls under the "influence" of the quantifier. Parentheses play an important role in determining the scope of quantifiers. For example, in
∀x(P(x)⟶Q(x))⟶S(x) the scope of the quantifier extends only over P(x)⟶Q(x) |
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Tautological Consequence
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A sentence S is a tautological consequence of some premises if S follows from the premise simply in virtue of meanings of the truth-functional connectives. We can check for tautological consequence by means of truth tables, since S is a tautological consequence of of the premises if and only if every row of their joint truth tables that assigns true to each of premise also assigns true to S. All tautological consequences are logical consequences, but not all logical consequences are tautological consequences.
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Literal
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A literal is a sentence that is either an atomic sentence or the negation of an atomic sentence.
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Sound Argument
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An argument is sound if it is both valid and all its premises are true.
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Valid Argument
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An argument is valid when the conclusion must be true in any circumstance in which the premises are true.
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Transitive of a Relation
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"Larger than" or "Less than"
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Reflexive/Symmetry of a Relation
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"Same size" or "Same row"
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DeMorgan's Laws
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¬(P∧Q) ⇔(¬P∨¬Q)
¬(P∨Q)⇔(¬P∧¬Q) |
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What reasons do the authors of your textbook give for thinking that the laws of logic are not matters of convention?
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In the book, it is said that the laws of logic are more fundamental and less subject to repeal, than the laws of the land or the laws of physics.
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What method, also used in science, does modern logic apply?
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Astronomy, economics, finance, law, mathematics, medicine, physics, and sociology
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Why learn an artificial language?
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It is important because artificial languages like FOL are used by mathematicans, philosophers, computer scientists, linguists, and practitioners of artificial intelligence. It is considered a universal language.
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What important features of names and predicates symbols in FOL must you keep in mind?
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There are different versions of FOL that have their own names and predicates for their own situations. (more?)
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How do you show that a conclusion is not a consequence of its premisses?
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When the conclusion has nothing to do with the premisses, then we can say that the conclusion is not a consequence.
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Why, although it appears on the "Rule? Menu" in Fitch is Ana Con not really a rule?
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Ana Con is really a mechanism that allows you to check for consequences among atomic sentences that involve many of the predicates in the blocks world language.
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Under what circumstances is an FOL sentence a good translation of an English sentence and why is a sentence not necessarily a good translation if it is true in the world it describes?
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idk
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What features of FOL should one be cautious about assuming are feature of English and why?
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idk
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What valid conclusion can one draw from inconsistent premisses? Why? What sound conclusions can one draw from inconsistent premisses? Why?
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idk
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