4. Propositional Logic Using truth tables
... Suppose A is a propositional formula in which the proposition symbols p0,…,pn-1 occur. Let Ai be for each i=0,…,n-1 an arbitrary propositional formula. Let A’ be the result of substituting everywhere in A the formula Ai for pi. ...
... Suppose A is a propositional formula in which the proposition symbols p0,…,pn-1 occur. Let Ai be for each i=0,…,n-1 an arbitrary propositional formula. Let A’ be the result of substituting everywhere in A the formula Ai for pi. ...
Document
... If a bird is the largest of all birds, then it is flightless. If a bird is the smallest bird, then it has a nest the size of a walnut half-shell. A. If a bird is the fastest bird on land, then it is an ostrich. (use 1 and 2.) B. If a bird is a hummingbird, then it has a nest the size of a walnut hal ...
... If a bird is the largest of all birds, then it is flightless. If a bird is the smallest bird, then it has a nest the size of a walnut half-shell. A. If a bird is the fastest bird on land, then it is an ostrich. (use 1 and 2.) B. If a bird is a hummingbird, then it has a nest the size of a walnut hal ...
Mathematical Logic
... The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-exponential number of steps. To check if A is a tautology, we have to con ...
... The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-exponential number of steps. To check if A is a tautology, we have to con ...
Propositional logic, I
... Inference rules: Typographical rules (they do not use meaning) to construct new sentences from a given group of sentences. Semantics: Interpretation rules that associate sentences in the language with statements in the domain of discourse. Forget meaning. Think of logic as a game. BEWARE: It is easy ...
... Inference rules: Typographical rules (they do not use meaning) to construct new sentences from a given group of sentences. Semantics: Interpretation rules that associate sentences in the language with statements in the domain of discourse. Forget meaning. Think of logic as a game. BEWARE: It is easy ...
Section 1
... Section 1.3 Truthtellers, liars and propositional logic We call a sentence a proposition ...
... Section 1.3 Truthtellers, liars and propositional logic We call a sentence a proposition ...
What is...Linear Logic? Introduction Jonathan Skowera
... guess would be acts of reasoning. With this in mind, it is not clear at first glance that linear logic falls in the domain of logic. The logic is called linear logic, and its rules of inference treat formulas as much like finite resources as propositions. That is a radical difference. With intuition ...
... guess would be acts of reasoning. With this in mind, it is not clear at first glance that linear logic falls in the domain of logic. The logic is called linear logic, and its rules of inference treat formulas as much like finite resources as propositions. That is a radical difference. With intuition ...
10a
... logically follow from a set of sentences (KB) • An inference rule is sound if every sentence X it produces when operating on a KB logically follows from the KB –i.e., inference rule creates no contradictions • An inference rule is complete if it can produce every expression that logically follows fr ...
... logically follow from a set of sentences (KB) • An inference rule is sound if every sentence X it produces when operating on a KB logically follows from the KB –i.e., inference rule creates no contradictions • An inference rule is complete if it can produce every expression that logically follows fr ...
1.2 Three definitions of “bit”: (1)
... OK Although we use this word hundreds of times a week whether things are OK or not, we have probably rarely wondered about its history. That history is in fact a brief one, the word being first recorded in 1839, though it was no doubt in circulation before then. Much scholarship has been expended on ...
... OK Although we use this word hundreds of times a week whether things are OK or not, we have probably rarely wondered about its history. That history is in fact a brief one, the word being first recorded in 1839, though it was no doubt in circulation before then. Much scholarship has been expended on ...
Logic and Proof
... – Every new red object would need a different proposition, e.g. “a cat is red” – There is no “formal connection” between propositions – Similarly, “a cat is fat” and “a cat is striped” – Similarly, “Bill loves Jill”, “Will loves Jill”, “Jill loves Phil” – What about representing quantifiers? “Someon ...
... – Every new red object would need a different proposition, e.g. “a cat is red” – There is no “formal connection” between propositions – Similarly, “a cat is fat” and “a cat is striped” – Similarly, “Bill loves Jill”, “Will loves Jill”, “Jill loves Phil” – What about representing quantifiers? “Someon ...
Propositional logic, I (Lógica Proposicional, I)
... Example: Block-lifting robot in block’s world Features x1(BATTERY_OK), x2 (LIFTABLE) x3 (MOVES) Robot can sense BATTERY_OK, MOVES, but not LIFTABLE Knowledge: BATTERY_OK ∧ LIFTABLE ⇒ MOVES. Robot reads {BATTERRY_OK (1), MOVES(0)} ...
... Example: Block-lifting robot in block’s world Features x1(BATTERY_OK), x2 (LIFTABLE) x3 (MOVES) Robot can sense BATTERY_OK, MOVES, but not LIFTABLE Knowledge: BATTERY_OK ∧ LIFTABLE ⇒ MOVES. Robot reads {BATTERRY_OK (1), MOVES(0)} ...
Diagrams in logic and mathematics - CFCUL
... “the laws of logic are not sculpted in stone, eternal and immutable. A realistic look at the development of mathematics shows that the reasons for a theorem are found only after digging deep and focusing upon the possibility of a theorem. The discovery of such hidden reasons is the work of the mathe ...
... “the laws of logic are not sculpted in stone, eternal and immutable. A realistic look at the development of mathematics shows that the reasons for a theorem are found only after digging deep and focusing upon the possibility of a theorem. The discovery of such hidden reasons is the work of the mathe ...
Conditional and Indirect Proofs
... • Tautologies are sometimes termed theorems of logic. • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This i ...
... • Tautologies are sometimes termed theorems of logic. • A tautology will follow from any premises whatever. • This is because the negation of a tautology is a contradiction, so if we use IP by assuming the negation of a tautology, we can derive a contradiction independently of other premises. This i ...
Lecture Notes 3
... for one of them but not both We can define exclusive or using ^ and v: P xor Q equiv: (P ^ ~Q) v (Q ^ ~P) (Vote(I,smith) ^ ~Vote(I,jones)) v (Vote(I,jones) ^ ~Vote(I,smith)) Unless the text says otherwise, assume inclusive “or” (even when it says “Either A or B”) ...
... for one of them but not both We can define exclusive or using ^ and v: P xor Q equiv: (P ^ ~Q) v (Q ^ ~P) (Vote(I,smith) ^ ~Vote(I,jones)) v (Vote(I,jones) ^ ~Vote(I,smith)) Unless the text says otherwise, assume inclusive “or” (even when it says “Either A or B”) ...
Identity and Philosophical Problems of Symbolic Logic
... Sentential logic is a two-valued truth-functional logic. But it has been argued that most natural language sentences do not have two truth-values. ...
... Sentential logic is a two-valued truth-functional logic. But it has been argued that most natural language sentences do not have two truth-values. ...