A BRIEF INTRODUCTION TO MODAL LOGIC Introduction Consider
... This claim has come to be seen as false. After all, if two statements are equivalent, they ought to imply each other. It seems reasonable to say that if P is the case then P must be a possible state of affairs, since what is true cannot be impossible. However, it is quite a bit less obvious to say t ...
... This claim has come to be seen as false. After all, if two statements are equivalent, they ought to imply each other. It seems reasonable to say that if P is the case then P must be a possible state of affairs, since what is true cannot be impossible. However, it is quite a bit less obvious to say t ...
Practice Problem Set 1
... 10. [From Endsem, Autumn 2011] Consider an employee relational database containing three tables R1 , R2 and R3 , each with two columns. The columns of R1 are labeled “Name” and “ID”, those of R2 are labeled “ID” and “Dept”, while those of R3 are labeled “Name” and “Name”. Table R1 gives the associat ...
... 10. [From Endsem, Autumn 2011] Consider an employee relational database containing three tables R1 , R2 and R3 , each with two columns. The columns of R1 are labeled “Name” and “ID”, those of R2 are labeled “ID” and “Dept”, while those of R3 are labeled “Name” and “Name”. Table R1 gives the associat ...
A General Proof Method for ... without the Barcan Formula.*
... necessity and possibility, but they can also provide a basis for reasoning about knowledge, belief, time and change, e.g. [Halpern & Moses, 19851. Automated reasoning in modal logics is made difficult, however, by (i) the absence of a normal form for expressions containing modal operators, and (ii) ...
... necessity and possibility, but they can also provide a basis for reasoning about knowledge, belief, time and change, e.g. [Halpern & Moses, 19851. Automated reasoning in modal logics is made difficult, however, by (i) the absence of a normal form for expressions containing modal operators, and (ii) ...
A Note on Assumptions about Skolem Functions
... [11] yields no search anymore. Every possible resolution step contributes to the proof. 3.2. Modal Logic Modal Logic is an extension of predicate logic with the two operators 2 and 3 [1]. The standard Kripke semantics of normal modal systems interprets the 2-operator as a universal quantification ov ...
... [11] yields no search anymore. Every possible resolution step contributes to the proof. 3.2. Modal Logic Modal Logic is an extension of predicate logic with the two operators 2 and 3 [1]. The standard Kripke semantics of normal modal systems interprets the 2-operator as a universal quantification ov ...
PHIL12A Section answers, 9 February 2011
... means that there are 28 = 256 possible ways to draw up such a truth table, and so there are 256 different ternary connectives. Good luck coming up with English equivalents! 3. The set of sentential connectives {¬, ∧, ∨} is complete. This means that every possible sentence using binary sentential con ...
... means that there are 28 = 256 possible ways to draw up such a truth table, and so there are 256 different ternary connectives. Good luck coming up with English equivalents! 3. The set of sentential connectives {¬, ∧, ∨} is complete. This means that every possible sentence using binary sentential con ...
p q
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
... Common phrasings for the biconditional • p if and only if q • p is necessary and equivalent for q • p is equivalent to q ...
CS173: Discrete Math
... discrete mathematics (q when p) – For Maria to get a good job, it is sufficient for her to learn discrete mathematics (sufficient condition for q is p) – Maria will find a good job unless she does not learn discrete mathematics (q unless not p) ...
... discrete mathematics (q when p) – For Maria to get a good job, it is sufficient for her to learn discrete mathematics (sufficient condition for q is p) – Maria will find a good job unless she does not learn discrete mathematics (q unless not p) ...
CS173: Discrete Math
... – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
... – This statement is true • If you buy a ticket and take the flight • If you do not buy a ticket and you cannot take the flight ...
Extending modal logic
... This means adding axioms to the logic. The good properties of the basic modal logic may or may not ...
... This means adding axioms to the logic. The good properties of the basic modal logic may or may not ...
Sub-Birkhoff
... name with its rule is called an axiom. Subequational logics generate subequational theories. Definition 2 For a subequational logic L = hS,Ii its theory L is generated by the following inference rules, where an inference rule (i) only applies if i ∈ I. s, t and r range over terms. `sLs ...
... name with its rule is called an axiom. Subequational logics generate subequational theories. Definition 2 For a subequational logic L = hS,Ii its theory L is generated by the following inference rules, where an inference rule (i) only applies if i ∈ I. s, t and r range over terms. `sLs ...
CS 40: Foundations of Computer Science
... to follow from our assumptions, so let's find a case in which the assumptions hold but this conditional statement does not. This conditional statement fails in the case in which s is true and e is false. If we take d to be true as well, then both of our assumptions are true. There fore this conclusi ...
... to follow from our assumptions, so let's find a case in which the assumptions hold but this conditional statement does not. This conditional statement fails in the case in which s is true and e is false. If we take d to be true as well, then both of our assumptions are true. There fore this conclusi ...
(P Q). - Snistnote
... Deals with the methods of reasoning. Provides rules and techniques for determining whether a given argument is valid. Concerned with all kinds of reasonings ...
... Deals with the methods of reasoning. Provides rules and techniques for determining whether a given argument is valid. Concerned with all kinds of reasonings ...
Tautologies Arguments Logical Implication
... • Do we have to try all 2k truth assignments (where k = #primitive propositions in A1, . . . , An, B). It’s not that bad. • Because of the way we defined ⇒, A1 ∧ . . . ∧ An ⇒ B is guaranteed to be true if A1 ∧ . . . ∧ An is false. • But if A1 ∧ . . . ∧ An is true, B is true, since the argument is va ...
... • Do we have to try all 2k truth assignments (where k = #primitive propositions in A1, . . . , An, B). It’s not that bad. • Because of the way we defined ⇒, A1 ∧ . . . ∧ An ⇒ B is guaranteed to be true if A1 ∧ . . . ∧ An is false. • But if A1 ∧ . . . ∧ An is true, B is true, since the argument is va ...
study guide.
... • Quantifiers For a predicate P (x), a quantified statement “for all” (“every”, “all”) ∀xP (x) is true iff P (x) is true for every value of x from the domain (also called universe); here, ∀ is called a universal quantifier. A statement “exists” (“some”, “a”) ∃xP (x) is true whenever P (x) is true fo ...
... • Quantifiers For a predicate P (x), a quantified statement “for all” (“every”, “all”) ∀xP (x) is true iff P (x) is true for every value of x from the domain (also called universe); here, ∀ is called a universal quantifier. A statement “exists” (“some”, “a”) ∃xP (x) is true whenever P (x) is true fo ...
Modal Logic
... or false in any model. But there are situations were we need to distinguish between different modes of truth, such as necessarily true, known to be true, believed to be true and always true in the future (with respect to time). For example, consider the sentence ”The math department is located on th ...
... or false in any model. But there are situations were we need to distinguish between different modes of truth, such as necessarily true, known to be true, believed to be true and always true in the future (with respect to time). For example, consider the sentence ”The math department is located on th ...
Logical Implications
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
... The conditional if-then used in several programming languages should not be confused with logical implications. Suppose we encounter if p then S in some programming language, the statement S will be executed if p is true. If p is false, statement S will not be executed. In general, S is not a statem ...
Exam 2 Sample
... 8. (10 pts) Simplify the given statement by moving the negation as "far inside" as possible, keeping the same meaning. Don't apply any definitions, just use the rules for negating quantifiers and logical operations. a. ~ ( For all x, y, z in A, if x R y and y R z, then x R z. ) b. ~ ( There exist x, ...
... 8. (10 pts) Simplify the given statement by moving the negation as "far inside" as possible, keeping the same meaning. Don't apply any definitions, just use the rules for negating quantifiers and logical operations. a. ~ ( For all x, y, z in A, if x R y and y R z, then x R z. ) b. ~ ( There exist x, ...
