Conditional Statements
... Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
... Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. ...
CHAPTER 1. SENTENTIAL LOGIC 1. Introduction In sentential logic
... The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, odd, prime all have their usual meanings then 7 is odd and 2 is odd is false but (7 is odd and 2 is odd) or 2 is prime is true. We will discuss implication later. ...
... The truth value of any compound sentence is determined completely by the truth values of its component parts. For example, assuming 2, 7, odd, prime all have their usual meanings then 7 is odd and 2 is odd is false but (7 is odd and 2 is odd) or 2 is prime is true. We will discuss implication later. ...
The Closed World Assumption
... We view our program as a logical theory expressing knowledge about the world. In several situations, it is convenient to assume that the program contains complete information about certain kinds of logical statements. We can then make additional inferences about the world based on the assumed comple ...
... We view our program as a logical theory expressing knowledge about the world. In several situations, it is convenient to assume that the program contains complete information about certain kinds of logical statements. We can then make additional inferences about the world based on the assumed comple ...
1. Kripke`s semantics for modal logic
... designate the same objects in all possible worlds. On the other hand, the term “Nixon” is just a name of this man’. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact h ...
... designate the same objects in all possible worlds. On the other hand, the term “Nixon” is just a name of this man’. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact h ...
1
... (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all variables occurring in a formula φ, then |=U φ [s] iff |=U φ [s0 ] for all formulas φ and interpretations U. (You may assume that the language has only the connectives ¬ and → and that ∀ ...
... (c) Prove the following by induction (on construction of formulas): if variable assignments s and s0 agree on all variables occurring in a formula φ, then |=U φ [s] iff |=U φ [s0 ] for all formulas φ and interpretations U. (You may assume that the language has only the connectives ¬ and → and that ∀ ...
3 The semantics of pure first
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
3 The semantics of pure first
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
Logical Consequence by Patricia Blanchette Basic Question (BQ
... that assign “true” to formulas in second order logic asserting the existence of sets with a cardinality between that of and that of , and the following statement: (X)(X > → ≤ X) ...
... that assign “true” to formulas in second order logic asserting the existence of sets with a cardinality between that of and that of , and the following statement: (X)(X > → ≤ X) ...
Incompleteness - the UNC Department of Computer Science
... characteristics which set him apart from the majority of mathematicians. One was his lack of rigor. Very often he would simply state a result which, he would insist, had just come to him from a vague, intuitive source, far out of the realm of conscious probing. In fact, he often said that the goddes ...
... characteristics which set him apart from the majority of mathematicians. One was his lack of rigor. Very often he would simply state a result which, he would insist, had just come to him from a vague, intuitive source, far out of the realm of conscious probing. In fact, he often said that the goddes ...
The Fundamental Theorem of World Theory
... r, and F, G, H will range over 0- and 1-place predicates, respectively. Lower case Greek letters may be used as metavariables as well, typically when a variable is needed to range over more than one syntactic class. Additionally, L contains a distinguished 1-place predicate constant A! which, intuit ...
... r, and F, G, H will range over 0- and 1-place predicates, respectively. Lower case Greek letters may be used as metavariables as well, typically when a variable is needed to range over more than one syntactic class. Additionally, L contains a distinguished 1-place predicate constant A! which, intuit ...
Maximal Introspection of Agents
... be likely to satisfy (at least not in the syntactic treatment). We might also in many cases take (2) to be too strong, since (A3) excludes the possibility of an agent having a false belief (though, in other cases, when reasoning about agents, it seems appropriate to assume that the agents will never ...
... be likely to satisfy (at least not in the syntactic treatment). We might also in many cases take (2) to be too strong, since (A3) excludes the possibility of an agent having a false belief (though, in other cases, when reasoning about agents, it seems appropriate to assume that the agents will never ...
Section 3 - UCLA Department of Mathematics
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
... For sentential logic, valid formulas and tautologies are by definition the same. For predicate logic, the notion of a tautology is different from that of a valid formula. Consider: (1) ∀v1 P 1 v1 → ∀v1 P 1 v1 ; (2) ∀v1 P 1 v1 → ∃v1 P 1 v1 . Intuitively, (1) is valid just because of its truth-functio ...
IS IT EASY TO LEARN THE LOGIC
... For our purposes, 'A implies B' connotes the real logical relationship between A and B, but 'if A then B' is only a formal relationship is not necessarily true. Similarly we can distinguish conceptually between 'A equals B' and 'A if and only if B'. ...
... For our purposes, 'A implies B' connotes the real logical relationship between A and B, but 'if A then B' is only a formal relationship is not necessarily true. Similarly we can distinguish conceptually between 'A equals B' and 'A if and only if B'. ...
Thought and World - University of Pittsburgh
... If we take facts to be actual states of affairs, then (C) yields the familiar formulation of the correspondence theory: a thought is true iff it semantically corresponds to a fact. I should stress that the concepts of semantic correspondence and state of affairs used in (C) are not the ones that def ...
... If we take facts to be actual states of affairs, then (C) yields the familiar formulation of the correspondence theory: a thought is true iff it semantically corresponds to a fact. I should stress that the concepts of semantic correspondence and state of affairs used in (C) are not the ones that def ...
Semantic Minimalism and the Frege Point1 Speech act
... propose an interpretation of just those (canonical) sentences or utterances in which constructions of the relevant type—“It is probable that ...”, “It is good that ...”, “It is true that ...”, or whatever—are not part of any clause other than a complete sentence. It is noted that there are many othe ...
... propose an interpretation of just those (canonical) sentences or utterances in which constructions of the relevant type—“It is probable that ...”, “It is good that ...”, “It is true that ...”, or whatever—are not part of any clause other than a complete sentence. It is noted that there are many othe ...
ctl
... AG AF enabled •For every reachable state, for all paths starting at that state we must reach another state where enabled is asserted ...
... AG AF enabled •For every reachable state, for all paths starting at that state we must reach another state where enabled is asserted ...
