INTERPLAYS OF KNOWLEDGE AND NON
... So we have two logics and there are two non-interdefinable operators: knowledge (K) and non-contingency (∆). Thus, in order to talk about both at the same time, we need to put logics together into a single formalism. Whenever there are non-interdefinable concepts in a given situation, combining logi ...
... So we have two logics and there are two non-interdefinable operators: knowledge (K) and non-contingency (∆). Thus, in order to talk about both at the same time, we need to put logics together into a single formalism. Whenever there are non-interdefinable concepts in a given situation, combining logi ...
the role of logic in teaching, learning and analyzing proof
... of outmost importance for developing a sophisticated understanding of calculus notions such as limit and continuity; yet it is ‘one of the least often acquired and most rarely understood concepts at all levels, from secondary school on up even, in many cases, into graduate school’. They describe an ...
... of outmost importance for developing a sophisticated understanding of calculus notions such as limit and continuity; yet it is ‘one of the least often acquired and most rarely understood concepts at all levels, from secondary school on up even, in many cases, into graduate school’. They describe an ...
Aristotle, Boole, and Categories
... (iv) XeY (X empty-intersection-with Y) asserting no X are Y, or Y holds of no X, or not(XiY). Set-theoretically these are the binary relations of inclusion and nonempty intersection, which are considered positive, and their respective contradictories, considered negative. Contradiction as an operat ...
... (iv) XeY (X empty-intersection-with Y) asserting no X are Y, or Y holds of no X, or not(XiY). Set-theoretically these are the binary relations of inclusion and nonempty intersection, which are considered positive, and their respective contradictories, considered negative. Contradiction as an operat ...
Completeness in modal logic - Lund University Publications
... ordered triple < W, R, V > where W and R are as before, and V is an assignment of the truthvalues 1 and 0 to each atomic formula at every world in W. A formula Φ is true in a model iff it has value 1 in every world in W for some valuation V. Φ is valid in a frame iff it is true in every model based ...
... ordered triple < W, R, V > where W and R are as before, and V is an assignment of the truthvalues 1 and 0 to each atomic formula at every world in W. A formula Φ is true in a model iff it has value 1 in every world in W for some valuation V. Φ is valid in a frame iff it is true in every model based ...
ctl
... •For all reachable states, if req is asserted then we must reach a state where ack is asserted •AG is interpreted relative to the start state •AG selects all states reachable from start state •AF is interpreted relative to where req is asserted ...
... •For all reachable states, if req is asserted then we must reach a state where ack is asserted •AG is interpreted relative to the start state •AG selects all states reachable from start state •AF is interpreted relative to where req is asserted ...
Chapter 2
... where (i, j ) ∈ modn if the absolute value |i − j | of the difference of i and j is divisible by n. A partition of a nonempty set S is a family of sets {Si | i ∈ I } such that (1) ∪i∈I Si = S, (2) Si ∩ Sj = ∅ for i = j , and (3) Si = ∅ for i ∈ I . If R is an equivalence relation on S, then the fam ...
... where (i, j ) ∈ modn if the absolute value |i − j | of the difference of i and j is divisible by n. A partition of a nonempty set S is a family of sets {Si | i ∈ I } such that (1) ∪i∈I Si = S, (2) Si ∩ Sj = ∅ for i = j , and (3) Si = ∅ for i ∈ I . If R is an equivalence relation on S, then the fam ...
Resolution Proof System for First Order Logic
... Process for removing existential quantifiers. Delete each existential quantifier, then replace the resulting free variables by terms referred to as Skolem functions. ...
... Process for removing existential quantifiers. Delete each existential quantifier, then replace the resulting free variables by terms referred to as Skolem functions. ...
Fine`s Theorem on First-Order Complete Modal Logics
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...
Document
... connected using Boolean connectives and quantifiers. You can use theorems of Boolean logic in the proof. • For example, if the assertion is P or Q, you can show it as follows: Suppose P is not true. Then, Q must be true. • Similarly, to show P Q, you assume P is true. From this, show Q is true. To ...
... connected using Boolean connectives and quantifiers. You can use theorems of Boolean logic in the proof. • For example, if the assertion is P or Q, you can show it as follows: Suppose P is not true. Then, Q must be true. • Similarly, to show P Q, you assume P is true. From this, show Q is true. To ...
PDF
... where the symbols ¬, ∧, and ∨ in Lc are used as abbreviational tools (see the first remark). Then we see that the proposition makes sense. 4. Another way of getting around this issue is to come up with another axiom system for PLc that uses →, ¬, ∧, and ∨ as primitive logical connectives. Such an ax ...
... where the symbols ¬, ∧, and ∨ in Lc are used as abbreviational tools (see the first remark). Then we see that the proposition makes sense. 4. Another way of getting around this issue is to come up with another axiom system for PLc that uses →, ¬, ∧, and ∨ as primitive logical connectives. Such an ax ...
classden
... continuous functions from D to D. This guarantees that any object d ∈ D is also a function d : D → D and hence that it is meaningful to talk about d(d). Scott domains thus support the interpretation of self-application and in fact are essential for the interpretation of functional languages which ar ...
... continuous functions from D to D. This guarantees that any object d ∈ D is also a function d : D → D and hence that it is meaningful to talk about d(d). Scott domains thus support the interpretation of self-application and in fact are essential for the interpretation of functional languages which ar ...
Lecture Notes 3
... then c is larger than a. Since we are given that a is smaller than b, it follows that b must be larger than a. Moreover, since c is identical to b, it follows that c must be larger than a. QED ...
... then c is larger than a. Since we are given that a is smaller than b, it follows that b must be larger than a. Moreover, since c is identical to b, it follows that c must be larger than a. QED ...
Modular Sequent Systems for Modal Logic
... System K + Ẋ. Figure 1 shows the set of rules from which we form our deductive systems. System K is the set of rules {∧, ∨, 2, k, ctr}. We will look at extensions of System K with sets of rules Ẋ ⊆ {ḋ, ṫ, ḃ, 4̇, 5̇}. The rules in Ẋ are called structural modal rules. The 5̇-rule is a bit specia ...
... System K + Ẋ. Figure 1 shows the set of rules from which we form our deductive systems. System K is the set of rules {∧, ∨, 2, k, ctr}. We will look at extensions of System K with sets of rules Ẋ ⊆ {ḋ, ṫ, ḃ, 4̇, 5̇}. The rules in Ẋ are called structural modal rules. The 5̇-rule is a bit specia ...
LOGIC MAY BE SIMPLE Logic, Congruence - Jean
... Do simple logics have semantics?, p. 140 Conclusion: logic may be simple, p. 142 ...
... Do simple logics have semantics?, p. 140 Conclusion: logic may be simple, p. 142 ...
Chapter 1 - National Taiwan University
... we should be able to assign truth values to propositions such that all requirements are satisfied. In Example 2, we are lucky to have simple requirements where there are only 2 propositions p and q. In real world, there may be hundreds, even thousands of propositions in the requirements. How to find p ...
... we should be able to assign truth values to propositions such that all requirements are satisfied. In Example 2, we are lucky to have simple requirements where there are only 2 propositions p and q. In real world, there may be hundreds, even thousands of propositions in the requirements. How to find p ...
Nonmonotonic Reasoning - Computer Science Department
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
PPT
... Informal Definition: “Independence of Irrelevant Alternatives” (IIA) Philosopher Sidney Morgenbesser is ordering dessert. The waiter says they have apple and blueberry pie. Morgenbesser asks for apple. The waiter comes back out and says “Oh, we have cherry as well!” “In that case,” says Morgenbesse ...
... Informal Definition: “Independence of Irrelevant Alternatives” (IIA) Philosopher Sidney Morgenbesser is ordering dessert. The waiter says they have apple and blueberry pie. Morgenbesser asks for apple. The waiter comes back out and says “Oh, we have cherry as well!” “In that case,” says Morgenbesse ...
The Compactness Theorem 1 The Compactness Theorem
... Theorem. This will play an important role in the second half of the course when we study predicate logic. This is due to our use of Herbrand’s Theorem to reduce reasoning about formulas of predicate logic to reasoning about infinite sets of formulas of propositional logic. Before stating and proving ...
... Theorem. This will play an important role in the second half of the course when we study predicate logic. This is due to our use of Herbrand’s Theorem to reduce reasoning about formulas of predicate logic to reasoning about infinite sets of formulas of propositional logic. Before stating and proving ...