slides 4-up
... however: we cannot check equality of functions (otherwise Haskell would be able to solve the Collatz conjecture) ...
... however: we cannot check equality of functions (otherwise Haskell would be able to solve the Collatz conjecture) ...
Logic Circuits
... For example, we can assign an equivalence between mathematical value and electrical charge. The extent to which we can operate on that electrical charge via the capacitor and our measuring instruments is the degree to which we can perform analogous mathematical calculations. There are problems, howe ...
... For example, we can assign an equivalence between mathematical value and electrical charge. The extent to which we can operate on that electrical charge via the capacitor and our measuring instruments is the degree to which we can perform analogous mathematical calculations. There are problems, howe ...
Yogi`s Report
... Very small quantities of fluid are required for analysis and synthesis (about 1000 times smaller than usually used at macroscopic levels). This is very beneficial for fluids which are difficult to obtain or are expensive. The sizes of the devices are so small that it makes them readily capable o ...
... Very small quantities of fluid are required for analysis and synthesis (about 1000 times smaller than usually used at macroscopic levels). This is very beneficial for fluids which are difficult to obtain or are expensive. The sizes of the devices are so small that it makes them readily capable o ...
Flowchart Thinking
... in your book is an example. Read this example and make sure you understand the proof. When a logical argument is complex or includes many steps, a paragraph proof may not be the clearest way to present the steps. In such cases, it is often helpful to organize the steps in the form of a flowchart. A ...
... in your book is an example. Read this example and make sure you understand the proof. When a logical argument is complex or includes many steps, a paragraph proof may not be the clearest way to present the steps. In such cases, it is often helpful to organize the steps in the form of a flowchart. A ...
Logic Circuits
... For example, we can assign an equivalence between mathematical value and electrical charge. The extent to which we can operate on that electrical charge via the capacitor and our measuring instruments is the degree to which we can perform analogous mathematical calculations. There are problems, howe ...
... For example, we can assign an equivalence between mathematical value and electrical charge. The extent to which we can operate on that electrical charge via the capacitor and our measuring instruments is the degree to which we can perform analogous mathematical calculations. There are problems, howe ...
Chapter 1 Section 2
... a computer science major or you are not a freshman.” One Solution: Let a, c, and f represent respectively “You can access the internet from campus,” “You are a computer science major,” and “You are a freshman.” a→ (c ∨ ¬ f ) ...
... a computer science major or you are not a freshman.” One Solution: Let a, c, and f represent respectively “You can access the internet from campus,” “You are a computer science major,” and “You are a freshman.” a→ (c ∨ ¬ f ) ...
pdf
... negation (¬), and the modal operator K. Call the resulting language LK 1 (Φ). (We often omit the Φ if it is clear from context or does not play a significant role.) As usual, we define ϕ∨ψ and ϕ ⇒ ψ as abbreviations of ¬(¬ϕ ∧ ¬ψ) and ¬ϕ ∨ ψ, respectively. The intended interpretation of Kϕ varies dep ...
... negation (¬), and the modal operator K. Call the resulting language LK 1 (Φ). (We often omit the Φ if it is clear from context or does not play a significant role.) As usual, we define ϕ∨ψ and ϕ ⇒ ψ as abbreviations of ¬(¬ϕ ∧ ¬ψ) and ¬ϕ ∨ ψ, respectively. The intended interpretation of Kϕ varies dep ...
Quantified Equilibrium Logic and the First Order Logic of Here
... Theorem 9 (Soundness) If Γ ⊢QHT α then Γ |=QHT α. If Γ ⊢QHTs α then Γ |=QHTs α. To prove the completeness of the systems, we will follow the Henkin method for intuitionistic logic. For this reason some details are omitted but they can be found, for instance, in [30]. Lemma 10 If Γ is a set of formu ...
... Theorem 9 (Soundness) If Γ ⊢QHT α then Γ |=QHT α. If Γ ⊢QHTs α then Γ |=QHTs α. To prove the completeness of the systems, we will follow the Henkin method for intuitionistic logic. For this reason some details are omitted but they can be found, for instance, in [30]. Lemma 10 If Γ is a set of formu ...
Logic
... • Formal logic is the science of deduction. • It aims to provide systematic means for telling whether or not given conclusions follow from given premises, i.e., whether arguments are valid or not ...
... • Formal logic is the science of deduction. • It aims to provide systematic means for telling whether or not given conclusions follow from given premises, i.e., whether arguments are valid or not ...
Hierarchical Introspective Logics
... systems not adequate for the proof of general propositions of "number theory", for example the "calculus of sentences", can be complete. For systems with a narrower scope of applicability completeness does not introduce paradoxes.) If a Goedel or Goedel-Rosser assertion is added to one of these inc ...
... systems not adequate for the proof of general propositions of "number theory", for example the "calculus of sentences", can be complete. For systems with a narrower scope of applicability completeness does not introduce paradoxes.) If a Goedel or Goedel-Rosser assertion is added to one of these inc ...
Principles of Computer Architecture Dr. Mike Frank
... transistor even during any onoff transition! – Why: When partially turned on, the transistor has relatively low R, gets high P=V2/R dissipation. – Corollary: Never turn off a transistor if it has a ...
... transistor even during any onoff transition! – Why: When partially turned on, the transistor has relatively low R, gets high P=V2/R dissipation. – Corollary: Never turn off a transistor if it has a ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.