A Logical Framework for Default Reasoning

... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...

... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...

AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY

... Here, S(a/x) is the interpretation which is exactly like S, except for assigning the object a to the variable x as its value. Montague now asks the same question as Kanger: How can this definition of the truthrelation ‚ be generalized to first-order languages with modal operators? As we recall, Kang ...

... Here, S(a/x) is the interpretation which is exactly like S, except for assigning the object a to the variable x as its value. Montague now asks the same question as Kanger: How can this definition of the truthrelation ‚ be generalized to first-order languages with modal operators? As we recall, Kang ...

The History of Categorical Logic

... Mac Lane at that point. In that respect, categories had an ambiguous status. It is clear that categories are conceptually required for the systematic and rigorous definition of natural transformations, but at the same time, they cannot be legitimate mathematical entities unless certain precautions a ...

... Mac Lane at that point. In that respect, categories had an ambiguous status. It is clear that categories are conceptually required for the systematic and rigorous definition of natural transformations, but at the same time, they cannot be legitimate mathematical entities unless certain precautions a ...

Fichte`s Legacy in Logic

... inferential system. In Herbart’s logic, existential judgments were quite literally tacked on as a final section in the logic of judgment, following a faithful replication of Kant’s synthetic treatment in accordance with the table of forms. The task of integrating this addition was taken up in detail ...

... inferential system. In Herbart’s logic, existential judgments were quite literally tacked on as a final section in the logic of judgment, following a faithful replication of Kant’s synthetic treatment in accordance with the table of forms. The task of integrating this addition was taken up in detail ...

popl13

... （function-oriented imperative language） • Features of functional languages: functions are first class values – A function can be created using an expression – Functions can take functions as their arguments. – Functions can return functions. ...

... （function-oriented imperative language） • Features of functional languages: functions are first class values – A function can be created using an expression – Functions can take functions as their arguments. – Functions can return functions. ...

A Representation Theorem for Second-Order Functionals

... Concretely, we show how coalgebras of a specific parameterised comonad are related to very well-behaved lenses (Section 4), and how traversable functors, subjected to certain coherence laws, are exactly the finitary containers (Section 5). Finally we show how the representation theorem can help when ...

... Concretely, we show how coalgebras of a specific parameterised comonad are related to very well-behaved lenses (Section 4), and how traversable functors, subjected to certain coherence laws, are exactly the finitary containers (Section 5). Finally we show how the representation theorem can help when ...

Nominal Monoids

... words w, w0 ∈ D∗ are equivalent if and only if: either both belong to Ldd , or both have the same first and last letters. Since there are infinitely many letters, there are infinitely many equivalence classes. Instead of studying finite monoids, we study something called orbit-finite monoids. Intuit ...

... words w, w0 ∈ D∗ are equivalent if and only if: either both belong to Ldd , or both have the same first and last letters. Since there are infinitely many letters, there are infinitely many equivalence classes. Instead of studying finite monoids, we study something called orbit-finite monoids. Intuit ...

Recursive Predicates And Quantifiers

... Still another application is made, when we consider the nature of a constructive existence proof. It appears that there is a proposition provable classically for which no constructive proof is possible (Theorem X). The endeavor has been made to include a fairly complete exposition of definitions and ...

... Still another application is made, when we consider the nature of a constructive existence proof. It appears that there is a proposition provable classically for which no constructive proof is possible (Theorem X). The endeavor has been made to include a fairly complete exposition of definitions and ...

funprog

... E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled sep ...

... E1, E2,...,En - E1 should evaluate to a function and then apply the function value of E1 to the arguments given by the values of E2,...,En. In the base case, there are self evaluating expressions (e.g. numbers and symbols). In addition, various special forms such as quote and if must be handled sep ...

Slide 1

... exists : ('a -> bool) -> 'a list -> bool for_all : ('a -> bool) -> 'a list -> bool map : ('a -> 'b) -> 'a list -> 'b list filter : ('a -> bool) -> 'a list -> 'a list iter : ('a -> unit) -> 'a list -> unit ...

... exists : ('a -> bool) -> 'a list -> bool for_all : ('a -> bool) -> 'a list -> bool map : ('a -> 'b) -> 'a list -> 'b list filter : ('a -> bool) -> 'a list -> 'a list iter : ('a -> unit) -> 'a list -> unit ...

Appendix B FUNCTIONAL PROGRAMMING WITH SCHEME

... expressions. This anomaly is caused by the side effect in the expression being evaluated, but programming by effect lies at the heart of imperative programming. If we depend on imperative programs, we must discard many of the basic properties of mathematics, such as associative and commuative laws o ...

... expressions. This anomaly is caused by the side effect in the expression being evaluated, but programming by effect lies at the heart of imperative programming. If we depend on imperative programs, we must discard many of the basic properties of mathematics, such as associative and commuative laws o ...

... substitution T, either T[O] is not valid or ~ [ c p ] is valid. In principle, this information can be obtained from looking at a list of all valid formulas. Similarly, in a logic with a notion of material implication, the truth inference rs I-, cp is sound iff the formula (T * cp is valid. Again, we ...

Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e

... structures whose accessibility relation is reflexive, symmetric and transitive. A sentence Kϕ is true in a world w belonging to M if ϕ is true in all worlds w0 belonging to M. However, not every universal S5-structure that satisfies the initial assumptions I of the agent is taken into consideration: ...

... structures whose accessibility relation is reflexive, symmetric and transitive. A sentence Kϕ is true in a world w belonging to M if ϕ is true in all worlds w0 belonging to M. However, not every universal S5-structure that satisfies the initial assumptions I of the agent is taken into consideration: ...

BL044389393

... switch driving, square/triangular-wave generation, and pulse-edge generation. HERE a new design of comparator is described with the help of Full adder which are the basic building block of ALU and ALU is a basic functioning unit of the microprocessors and DSP. The objective of this paper is to provi ...

... switch driving, square/triangular-wave generation, and pulse-edge generation. HERE a new design of comparator is described with the help of Full adder which are the basic building block of ALU and ALU is a basic functioning unit of the microprocessors and DSP. The objective of this paper is to provi ...

# 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.