Chapter 8
... • A mercury switch (also known as a mercury tilt switch) is a switch which opens and closes an electrical circuit through a small amount of liquid mercury. • Mercury switches have one or more sets of electrical contacts in a sealed glass envelope which contains a bead of mercury. • The envelope may ...
... • A mercury switch (also known as a mercury tilt switch) is a switch which opens and closes an electrical circuit through a small amount of liquid mercury. • Mercury switches have one or more sets of electrical contacts in a sealed glass envelope which contains a bead of mercury. • The envelope may ...
Formal Foundations of Computer Security
... is typed, and polymorphic operations are allowed. We need not assume decidability of equality on message contents, but it must be possible to decide whether tags are equal. Processes In our formal computing model, processes are called message automata (MA). Their state is potentially infinite and co ...
... is typed, and polymorphic operations are allowed. We need not assume decidability of equality on message contents, but it must be possible to decide whether tags are equal. Processes In our formal computing model, processes are called message automata (MA). Their state is potentially infinite and co ...
full text (.pdf)
... A Kleene algebra with tests is dened simply as a Kleene algebra with an embedded Boolean subalgebra. Possible interpretations include the various standard relational and trace-based models used in program semantics, and KAT is complete for the equational theory of these models Kozen and Smith 1996 ...
... A Kleene algebra with tests is dened simply as a Kleene algebra with an embedded Boolean subalgebra. Possible interpretations include the various standard relational and trace-based models used in program semantics, and KAT is complete for the equational theory of these models Kozen and Smith 1996 ...
3.1.3 Subformulas
... Definition 3.8 Let F be a propositional formula. The set of subformulas of F is the smallest set S(F ) satisfying the following conditions: 1. F ∈ S(F ). 2. If ¬G ∈ S(F ) , then G ∈ S(F ). 3. If (G1 ◦ G2 ) ∈ S(F ) , then G1 , G2 ∈ S(F ). It will be shown in Exercise 3.4 that such a smallest set exis ...
... Definition 3.8 Let F be a propositional formula. The set of subformulas of F is the smallest set S(F ) satisfying the following conditions: 1. F ∈ S(F ). 2. If ¬G ∈ S(F ) , then G ∈ S(F ). 3. If (G1 ◦ G2 ) ∈ S(F ) , then G1 , G2 ∈ S(F ). It will be shown in Exercise 3.4 that such a smallest set exis ...
Computers and Logic/Boolean Operators
... Boolean Logic / Boolean Algebra Applying Boolean Logic to computers allows them to handle very complex problems using complicated connections of simple components. ...
... Boolean Logic / Boolean Algebra Applying Boolean Logic to computers allows them to handle very complex problems using complicated connections of simple components. ...
Logic gate circuits
... elements called Digital Logic Gates that perform the logical operations of AND, OR and NOT on binary numbers. In digital logic only two voltage levels or states are allowed and these states are generally referred to as Logic "1" or Logic "0", High or Low, True or False and which are represented in B ...
... elements called Digital Logic Gates that perform the logical operations of AND, OR and NOT on binary numbers. In digital logic only two voltage levels or states are allowed and these states are generally referred to as Logic "1" or Logic "0", High or Low, True or False and which are represented in B ...
Q 0 - SSDI
... - The resultant Ri describes what is proved wrt to the initial query Q0, after i derivation steps. In particular Nothing has been proven in the begining R0: Q0 Q0 The query has been answered, if the derivation is successful Rn : Q0 θ1 θ2 ... θn if Qn = □ (since □ = true) ...
... - The resultant Ri describes what is proved wrt to the initial query Q0, after i derivation steps. In particular Nothing has been proven in the begining R0: Q0 Q0 The query has been answered, if the derivation is successful Rn : Q0 θ1 θ2 ... θn if Qn = □ (since □ = true) ...
When Bi-Interpretability Implies Synonymy
... We are interested in theories with coding. There are several ‘degrees’ of coding, like pairing, sequences, etcetera. We want a notion that allows us to build arbitrary sequences of all objects of our domain. The relevant notion is sequentiality. We also define a wider notion conceptuality. This last ...
... We are interested in theories with coding. There are several ‘degrees’ of coding, like pairing, sequences, etcetera. We want a notion that allows us to build arbitrary sequences of all objects of our domain. The relevant notion is sequentiality. We also define a wider notion conceptuality. This last ...
A Critique of the Foundations of Hoare-Style Programming Logics
... about certain programming constructs will probably. require a more flexible notation than Hoare's. ...
... about certain programming constructs will probably. require a more flexible notation than Hoare's. ...
A Critique of the Foundations of Hoare-Style
... about certain programming constructs will probably. require a more flexible notation than Hoare's. ...
... about certain programming constructs will probably. require a more flexible notation than Hoare's. ...
Primitive Recursive Arithmetic and its Role in the Foundations of
... is not that it concerns special domains of ‘constructive objects’ of higher type, but rather that it treats the higher types constructively.6 This means that Kronecker’s principle will be violated and the law of double negation elimination (i.e. classical propositional logic) will not in general be ...
... is not that it concerns special domains of ‘constructive objects’ of higher type, but rather that it treats the higher types constructively.6 This means that Kronecker’s principle will be violated and the law of double negation elimination (i.e. classical propositional logic) will not in general be ...
A proposition is any declarative sentence (including mathematical
... Definition: A tautology, or a law of propositional logic, is a statement which is always true A contradiction is a statement whose truth function has all Fs as outputs (in other words, it’s a statement whose negation is a tautology). Two statements are called propositionally equivalent if a tautolog ...
... Definition: A tautology, or a law of propositional logic, is a statement which is always true A contradiction is a statement whose truth function has all Fs as outputs (in other words, it’s a statement whose negation is a tautology). Two statements are called propositionally equivalent if a tautolog ...
pdf
... Proof: Assume S has a closed tableau T and consider the set Sp of premises of T . By König’s lemma, T must be finite and so is Sp . Sp must be unsatisfiable, since otherwise every branch containing Sp would be open. Theorem: If all finite subsets of a denumerable set S of pure formulas are satisfia ...
... Proof: Assume S has a closed tableau T and consider the set Sp of premises of T . By König’s lemma, T must be finite and so is Sp . Sp must be unsatisfiable, since otherwise every branch containing Sp would be open. Theorem: If all finite subsets of a denumerable set S of pure formulas are satisfia ...
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.