Slide 1
... Logic and Bit Operations • Bit: binary digit • Boolean variable: either true or false – Can be represented by a bit ...
... Logic and Bit Operations • Bit: binary digit • Boolean variable: either true or false – Can be represented by a bit ...
Natural Deduction Proof System
... reflect the logical steps in an informal rigorous proof. For each connective there is an introduction rule (except conjunction, which has two) which can be seen as a definition of which conditions must be satisfied for the proposition to be true. ...
... reflect the logical steps in an informal rigorous proof. For each connective there is an introduction rule (except conjunction, which has two) which can be seen as a definition of which conditions must be satisfied for the proposition to be true. ...
Logic - UNM Computer Science
... When the voltage on base is high, the switch is open and current can flow from collector to the emitter. When the voltage on base is low or close to 0, the switch is turned off and no current can flow from the collector to the emitter. Using the transistor as a switch, we can build NAND gate. Figure ...
... When the voltage on base is high, the switch is open and current can flow from collector to the emitter. When the voltage on base is low or close to 0, the switch is turned off and no current can flow from the collector to the emitter. Using the transistor as a switch, we can build NAND gate. Figure ...
S. P. Odintsov “REDUCTIO AD ABSURDUM” AND LUKASIEWICZ`S
... only first of these two axioms.. In this way minimal logic is paraconsistent according to the generally accepted definition of paraconsistent logics as logics admitting inconsistent but non-trivial theories. But it lies on the border line of paraconsistency. Usually (see, e.g. [27]) the above definitio ...
... only first of these two axioms.. In this way minimal logic is paraconsistent according to the generally accepted definition of paraconsistent logics as logics admitting inconsistent but non-trivial theories. But it lies on the border line of paraconsistency. Usually (see, e.g. [27]) the above definitio ...
Document
... the resulting formula by the newly introduced quantifier. This is eliminated by the last clause in restriction 4 on UG. ...
... the resulting formula by the newly introduced quantifier. This is eliminated by the last clause in restriction 4 on UG. ...
Natural deduction for predicate logic
... This suggests that to prove a formula of the form ∀xφ, we can prove φ with some arbitrary but fresh variable x0 substituted for x. That is, we want to prove the formula φ[x0 /x]. On the previous slide, we used n as a fresh variable, but in our formal proofs, we adopt the convention of using subscri ...
... This suggests that to prove a formula of the form ∀xφ, we can prove φ with some arbitrary but fresh variable x0 substituted for x. That is, we want to prove the formula φ[x0 /x]. On the previous slide, we used n as a fresh variable, but in our formal proofs, we adopt the convention of using subscri ...
Notes on Propositional and Predicate Logic
... • Replace all occurrences of imp and eqv by expressions using and, or, and not. • Move all occurrences of not “inwards” using – (not (and p q)) == (or (not p)(not q)) – (not (or p q)) == (and (not p)(not q)) • Simplify all subexpressions of the form (not (not p)) to p • Move all occurrences of or “i ...
... • Replace all occurrences of imp and eqv by expressions using and, or, and not. • Move all occurrences of not “inwards” using – (not (and p q)) == (or (not p)(not q)) – (not (or p q)) == (and (not p)(not q)) • Simplify all subexpressions of the form (not (not p)) to p • Move all occurrences of or “i ...
The Logic of Conditionals
... So, once you see that Q is not a tautological consequence of P1,…,Pn, you can be sure that there is no way to FT-prove Q from P1,…,Pn. ...
... So, once you see that Q is not a tautological consequence of P1,…,Pn, you can be sure that there is no way to FT-prove Q from P1,…,Pn. ...
Identity in modal logic theorem proving
... metatheory, we use it to formulate the validity-conditions of the semantic metalanguage. To apply this semantic method, one starts with some basic semantic notion in terms of which the notion of validity is defined. One translates the object language sentence into one which characterizes it in terms ...
... metatheory, we use it to formulate the validity-conditions of the semantic metalanguage. To apply this semantic method, one starts with some basic semantic notion in terms of which the notion of validity is defined. One translates the object language sentence into one which characterizes it in terms ...
Curry`s paradox, Lukasiewicz, and Field
... they are the most natural. And they evidently can be carried over to a framework where we allow more than three values. But what are we to make of the suggestion that we should use more than three values? As I remarked before, in the original three-valued framework it would be better to say that the ...
... they are the most natural. And they evidently can be carried over to a framework where we allow more than three values. But what are we to make of the suggestion that we should use more than three values? As I remarked before, in the original three-valued framework it would be better to say that the ...
Robot Morality and Review of classical logic.
... Suppose your waiter tells you that you can have either rice pilaf or baked potato with your dinner. In such circumstances, he plainly does not mean either rice pilaf or baked potato or both. You have to choose. So this use of “or” doesn’t fit the definition of disjunction given above. ...
... Suppose your waiter tells you that you can have either rice pilaf or baked potato with your dinner. In such circumstances, he plainly does not mean either rice pilaf or baked potato or both. You have to choose. So this use of “or” doesn’t fit the definition of disjunction given above. ...
LCD_5
... In a positive logic system, a high voltage is used to represent logical true (1), and a low voltage for a logical false (0). • Negative Logic In a negative logic system, a low voltage is used to represent logical true (1), and a high voltage for a logical false (0). ...
... In a positive logic system, a high voltage is used to represent logical true (1), and a low voltage for a logical false (0). • Negative Logic In a negative logic system, a low voltage is used to represent logical true (1), and a high voltage for a logical false (0). ...
Computing Default Extensions by Reductions on OR
... needed for the Modal Reduction Theorem. Our approach to formalizing default logic is complementary to the approach in (Lakemeyer and Levesque 2006), in which it is the logic of O R that is axiomatized. Although this is, from the point of view of theoremhood, a stronger system than the rewriting syst ...
... needed for the Modal Reduction Theorem. Our approach to formalizing default logic is complementary to the approach in (Lakemeyer and Levesque 2006), in which it is the logic of O R that is axiomatized. Although this is, from the point of view of theoremhood, a stronger system than the rewriting syst ...
Propositional Logic Syntax of Propositional Logic
... • checking a set of sentences for satisfiability is NP-complete – but there are some circumstances where the proof only involves a small subset of the KB, so can do some of the work in polynomial time – if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by t ...
... • checking a set of sentences for satisfiability is NP-complete – but there are some circumstances where the proof only involves a small subset of the KB, so can do some of the work in polynomial time – if a KB is monotonic (i.e., even if we add new sentences to a KB, all the sentences entailed by t ...
( (ϕ ∧ ψ) - EEE Canvas
... this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can deduce ϕ ∧ ψ. ...
... this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can deduce ϕ ∧ ψ. ...
deductive system
... A deductive system is a formal (mathematical) setup of reasoning. In order to describe a deductive system, a (formal) language system must first be in place, consisting of (well-formed) formulas, strings of symbols constructed according to some prescribed syntax. With the language in place, reasonin ...
... A deductive system is a formal (mathematical) setup of reasoning. In order to describe a deductive system, a (formal) language system must first be in place, consisting of (well-formed) formulas, strings of symbols constructed according to some prescribed syntax. With the language in place, reasonin ...
Aristotle`s particularisation
... We have formally defined Aristotle’s particularisation, which is the postulation that an existentially quantified formula of a first order language S, such as ‘[(∃x)P (x)]’, can be assumed to always interpret as the proposition, ‘There exists some s in the domain D of the interpretation such that P ...
... We have formally defined Aristotle’s particularisation, which is the postulation that an existentially quantified formula of a first order language S, such as ‘[(∃x)P (x)]’, can be assumed to always interpret as the proposition, ‘There exists some s in the domain D of the interpretation such that P ...
Elements of Modal Logic - University of Victoria
... The logic pc has an associated system. Let Spc = (Apc , Rpc ), where Apc contains every instance of the formula schemas, [A1] α → (β → α) [A2] (α → (β → γ)) → ((α → β) → (α → γ)) [A3] (¬α → ¬β) → (β → α) and where Rpc contains the single rule modus ponens, [MP] α, α → β β It can be proved that L(S ...
... The logic pc has an associated system. Let Spc = (Apc , Rpc ), where Apc contains every instance of the formula schemas, [A1] α → (β → α) [A2] (α → (β → γ)) → ((α → β) → (α → γ)) [A3] (¬α → ¬β) → (β → α) and where Rpc contains the single rule modus ponens, [MP] α, α → β β It can be proved that L(S ...
Exercises: Sufficiently expressive/strong
... 1. Suppose T is an effectively axiomatized sound theory. Which of the following questions are you currently placed to settle? (a) Suppose G is a sentence of T ’s language which is true iff G is not provable in T : can T decide G? (b) Suppose H is a sentence of T ’s language which is true iff H is pr ...
... 1. Suppose T is an effectively axiomatized sound theory. Which of the following questions are you currently placed to settle? (a) Suppose G is a sentence of T ’s language which is true iff G is not provable in T : can T decide G? (b) Suppose H is a sentence of T ’s language which is true iff H is pr ...
Predicate logic, motivation
... result should never be an open sentence (i.e., no free variables allowed when translating). ...
... result should never be an open sentence (i.e., no free variables allowed when translating). ...
Identity and Philosophical Problems of Symbolic Logic
... logic. But it has been argued that most natural language sentences do not have two truth-values. ...
... logic. But it has been argued that most natural language sentences do not have two truth-values. ...