On Perfect Introspection with Quantifying-in
... replaced by ti. For the semantics, we need to specify when an atomic sentence is true and when a sentence is believed. The t r u t h of an arbitrary sentence is then defined by the usual recursive rules. While the t r u t h of atomic sentences is determined by worlds, belief is modeled in possiblewo ...
... replaced by ti. For the semantics, we need to specify when an atomic sentence is true and when a sentence is believed. The t r u t h of an arbitrary sentence is then defined by the usual recursive rules. While the t r u t h of atomic sentences is determined by worlds, belief is modeled in possiblewo ...
Three Solutions to the Knower Paradox
... Montague [9] and basically is the epistemological counterpart of the Liar Paradox. I will start by presenting it in its original version, the one which treats knowledge as a predicate attached to names of sentences and uses the framework of first order arithmetic. ...
... Montague [9] and basically is the epistemological counterpart of the Liar Paradox. I will start by presenting it in its original version, the one which treats knowledge as a predicate attached to names of sentences and uses the framework of first order arithmetic. ...
Tactics for Separation Logic Abstract Andrew W. Appel INRIA Rocquencourt & Princeton University
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
... proving an imperative program, much of the reasoning is not about memory cells but concerns the abstract mathematical objects that the program’s data structures represent. Lemmas about those objects are most conveniently proved in a general-purpose higher-order logic, especially when there are large ...
Chapter 7 Recursion
... The abstraction ( x. M) of a WFF M where x is a variable. When interpreted, this will be regarded as a function with one formal parameter called x. The value returned by the function is M (which will probably involve x). ...
... The abstraction ( x. M) of a WFF M where x is a variable. When interpreted, this will be regarded as a function with one formal parameter called x. The value returned by the function is M (which will probably involve x). ...
Lecture Notes on the Lambda Calculus
... 2. Gödel defined the class of general recursive functions as the smallest set of functions containing all the constant functions, the successor function, and closed under certain operations (such as compositions and recursion). He postulated that a function is computable (in the intuitive sense) i ...
... 2. Gödel defined the class of general recursive functions as the smallest set of functions containing all the constant functions, the successor function, and closed under certain operations (such as compositions and recursion). He postulated that a function is computable (in the intuitive sense) i ...
preliminary version
... is particularly striking for disjunctions: we can only conclude A ∨ B if we have a proof of A or a proof of B. Therefore, A ∨ ¬A is not a tautology of intuitionistic logic: it is not the case that for every proposition A we have either a proof of A or a proof of ¬A. In classical logic, the situation ...
... is particularly striking for disjunctions: we can only conclude A ∨ B if we have a proof of A or a proof of B. Therefore, A ∨ ¬A is not a tautology of intuitionistic logic: it is not the case that for every proposition A we have either a proof of A or a proof of ¬A. In classical logic, the situation ...
Lecture notes #2 - inst.eecs.berkeley.edu
... exactly is a proof? How do you show that a proposition is true? Recall that there are certain propositions called axioms or postulates, that we accept without proof (we have to start somewhere). A formal proof is a sequence of statements, ending with the proposition being proved, with the property t ...
... exactly is a proof? How do you show that a proposition is true? Recall that there are certain propositions called axioms or postulates, that we accept without proof (we have to start somewhere). A formal proof is a sequence of statements, ending with the proposition being proved, with the property t ...
Adiabatic Logic as Low-Power Design Technique for Biomedical
... recycled (reused) an infinite number of times Practically, this is not possible By adopting a real adiabatic logic, each charge can be recycled for many time so that a significant power dissipation reduction would be possible ...
... recycled (reused) an infinite number of times Practically, this is not possible By adopting a real adiabatic logic, each charge can be recycled for many time so that a significant power dissipation reduction would be possible ...
Electronic Troubleshooting
... • Logic symbol arrows indicate I/O • PR and CLR act like the Set (S) and Reset (R) inputs on a NAND Gate R-S Filip-Flop • Q and Q are always in opposite states • The input CK (clock) on a positive transition causes Q to go either high or low depending on the D input • Q’s state will match the state ...
... • Logic symbol arrows indicate I/O • PR and CLR act like the Set (S) and Reset (R) inputs on a NAND Gate R-S Filip-Flop • Q and Q are always in opposite states • The input CK (clock) on a positive transition causes Q to go either high or low depending on the D input • Q’s state will match the state ...
Lecture notes #2: Proofs - EECS: www
... exactly is a proof? How do you show that a proposition is true? Recall that there are certain propositions called axioms or postulates, that we accept without proof (we have to start somewhere). A formal proof is a sequence of statements, ending with the proposition being proved, with the property t ...
... exactly is a proof? How do you show that a proposition is true? Recall that there are certain propositions called axioms or postulates, that we accept without proof (we have to start somewhere). A formal proof is a sequence of statements, ending with the proposition being proved, with the property t ...
Syllogistic Logic with Complements
... next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each node is either an element of Γ or comes from its parent(s) by an application of one of the rules for the fragment listed in Figure 1. Γ ...
... next turn to the proof theory. A proof tree over Γ is a finite tree T whose nodes are labeled with sentences in our fragment, with the additional property that each node is either an element of Γ or comes from its parent(s) by an application of one of the rules for the fragment listed in Figure 1. Γ ...
PhysLimL24
... • About pipelined, sequential, fully-adiabatic CMOS logic: – Q: Does it require an intermediate voltage level? • A: No, you can get by with only 2 different levels. ...
... • About pipelined, sequential, fully-adiabatic CMOS logic: – Q: Does it require an intermediate voltage level? • A: No, you can get by with only 2 different levels. ...
Propositional inquisitive logic: a survey
... We mentioned above that in inquisitive logic, entailments involving questions capture logical dependencies. The relation of dependency is also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in ...
... We mentioned above that in inquisitive logic, entailments involving questions capture logical dependencies. The relation of dependency is also the focus of recent work in the framework of dependence logic [23]. Dependence logic and inquisitive logic are tightly connected frameworks, as discussed in ...
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.