KnotandTonk 1 Preliminaries
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
Equivalence of the information structure with unawareness to the
... constructed in Li (2009) bypasses the impossibility result by having the agent use a (possibly different) subjective state space at each state. The logic of awareness in Fagin and Halpern (1988) captures nontrivial unawareness by making the agent aware of only a subset of the propositions in the mod ...
... constructed in Li (2009) bypasses the impossibility result by having the agent use a (possibly different) subjective state space at each state. The logic of awareness in Fagin and Halpern (1988) captures nontrivial unawareness by making the agent aware of only a subset of the propositions in the mod ...
Propositional inquisitive logic: a survey
... for intuitionistic logic, this implies that anything that can be falsified in inquisitive logic can be falsified in intuitionistic propositional logic, IPL. On the other hand, it is easy to see that singleton information states {w} behave just like the corresponding propositional valuation w: this e ...
... for intuitionistic logic, this implies that anything that can be falsified in inquisitive logic can be falsified in intuitionistic propositional logic, IPL. On the other hand, it is easy to see that singleton information states {w} behave just like the corresponding propositional valuation w: this e ...
Integrating Logical Reasoning and Probabilistic Chain Graphs
... example illustrating this representation is shown below (Example 1). Atoms that do not occur as head of a clause are called assumables. From a logical point of view, the ‘:’ operator has the meaning of a conjunction; it is only included in the syntax to allow separating atoms that are templates from ...
... example illustrating this representation is shown below (Example 1). Atoms that do not occur as head of a clause are called assumables. From a logical point of view, the ‘:’ operator has the meaning of a conjunction; it is only included in the syntax to allow separating atoms that are templates from ...
LOGIC MAY BE SIMPLE Logic, Congruence - Jean
... by the development of abstract algebra (see [Dieudonné 1982], p. 619). It is worth noting that there was a time when “structure” was used to name what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is a strong tendency to consider universal algebra as a general theory ...
... by the development of abstract algebra (see [Dieudonné 1982], p. 619). It is worth noting that there was a time when “structure” was used to name what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is a strong tendency to consider universal algebra as a general theory ...
PPTX
... This means that our variables are not variable, i.e., cannot change their values! In other words, they are immutable and only represent some constant value. The execution of a program only involves the evaluation of functions. ...
... This means that our variables are not variable, i.e., cannot change their values! In other words, they are immutable and only represent some constant value. The execution of a program only involves the evaluation of functions. ...
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 ...
ML Basics
... Libraries usually contain functionals that can be customized. sort order list Can be used for: descending_order_sort ascending_order_sort sort_on_length sort_lexicographically sort_on_name sort_on_salary ...
... Libraries usually contain functionals that can be customized. sort order list Can be used for: descending_order_sort ascending_order_sort sort_on_length sort_lexicographically sort_on_name sort_on_salary ...
210ch2 - Dr. Djamel Bouchaffra
... Note: f associates with each x in A one and only one y in B. A is called the domain and B is called the codomain. If f(x) = y y is called the image of x under f x is called a preimage of y (note there may be more than one preimage of y but there is only one image of x). The range of f is the set of ...
... Note: f associates with each x in A one and only one y in B. A is called the domain and B is called the codomain. If f(x) = y y is called the image of x under f x is called a preimage of y (note there may be more than one preimage of y but there is only one image of x). The range of f is the set of ...
The Conception, Evolution, and Application of Functional
... most imperative languages is hopelessly weak (although there are important exceptions, such as Scheme [RCe86]). Rather than saying, then, what functional languages don’t have, it is better to characterize them by the features they do have. For modern functional languages, those features include high ...
... most imperative languages is hopelessly weak (although there are important exceptions, such as Scheme [RCe86]). Rather than saying, then, what functional languages don’t have, it is better to characterize them by the features they do have. For modern functional languages, those features include high ...
Principles of Programming Languages - 815338A
... • Efficiency is the primary concern, rather than the suitability of the language for software development ...
... • Efficiency is the primary concern, rather than the suitability of the language for software development ...
PPT
... Role of logic in mathematics • The original goal of formal logic was to axiomatize mathematics – Hilbert’s program (1920’s): find a formalization of mathematics that is: • Complete: any true sentence can be proved • Consistent: free from contradictions (no false sentence can be proved) • Decidable: ...
... Role of logic in mathematics • The original goal of formal logic was to axiomatize mathematics – Hilbert’s program (1920’s): find a formalization of mathematics that is: • Complete: any true sentence can be proved • Consistent: free from contradictions (no false sentence can be proved) • Decidable: ...
Example - bYTEBoss
... We can also define lambda expressions: ghci> let f n = (\x -> x+1) n ghci>f 20 ...
... We can also define lambda expressions: ghci> let f n = (\x -> x+1) n ghci>f 20 ...
Definability in Boolean bunched logic
... Proof. In each case we build models M and M 0 such that there is a bounded morphism from M to M 0 , but M has the property ...
... Proof. In each case we build models M and M 0 such that there is a bounded morphism from M to M 0 , but M has the property ...
08 – Functional Paradigm and Scheme
... To create a function in Scheme, we need to call the “define” function. “Define” expects two parameters: the first specifies the function’s signature, or prototype (i.e., it’s name and its incoming parameter(s)), and the second parameter specifies what the function should return. For example, here is ...
... To create a function in Scheme, we need to call the “define” function. “Define” expects two parameters: the first specifies the function’s signature, or prototype (i.e., it’s name and its incoming parameter(s)), and the second parameter specifies what the function should return. For example, here is ...
duality of quantifiers ¬8xA(x) 9x¬A(x) ¬9xA(x) 8x¬A(x)
... There are problems that cannot be solved by computer programs (i.e. algorithms) even assuming unlimited time and space. What is an “algorithm”? The following are all equivalent: - C programs, scheme programs, Java programs . . . - Turing machines (Turing’s idea of an “algorithm”) ...
... There are problems that cannot be solved by computer programs (i.e. algorithms) even assuming unlimited time and space. What is an “algorithm”? The following are all equivalent: - C programs, scheme programs, Java programs . . . - Turing machines (Turing’s idea of an “algorithm”) ...
Using linear logic to reason about sequent systems
... • Since the encodings yield abstract logic programming, procedures for proof search and unification in linear logic can be used to help fashion implementations of object-logics. • Since the encoding of proof systems is natural and direct, we hope to be able to use the rich meta-theory of linear logi ...
... • Since the encodings yield abstract logic programming, procedures for proof search and unification in linear logic can be used to help fashion implementations of object-logics. • Since the encoding of proof systems is natural and direct, we hope to be able to use the rich meta-theory of linear logi ...
First-Order Loop Formulas for Normal Logic Programs
... compute similar loops and loop formulas every time a program is grounded on a domain. Thus extending loop formulas in logic programming to first-order case is not only theoretically interesting, but may also be of practical relevance. Specifically, in this paper, we propose notions of firstorder loo ...
... compute similar loops and loop formulas every time a program is grounded on a domain. Thus extending loop formulas in logic programming to first-order case is not only theoretically interesting, but may also be of practical relevance. Specifically, in this paper, we propose notions of firstorder loo ...
An Operational Semantics for Declarative Multi
... the higher-order features of current functional languages can be reduced to firstorder definitions by introducing an auxiliary “apply” function [24]. Therefore, we base the definition of our operational semantics on the flat form described above. This is also consistent with current implementations ...
... the higher-order features of current functional languages can be reduced to firstorder definitions by introducing an auxiliary “apply” function [24]. Therefore, we base the definition of our operational semantics on the flat form described above. This is also consistent with current implementations ...
PROGRAMMING LANGUAGES 6.5 Higher Order Functions A
... Note again the difference in the inferred types of the functions. It is of course possible to define curried_fold by nesting occurrences of the explicit fn notation within the function’s body. The shorthand notation, however, is substantially more intuitive and convenient. Note also that Currying in ...
... Note again the difference in the inferred types of the functions. It is of course possible to define curried_fold by nesting occurrences of the explicit fn notation within the function’s body. The shorthand notation, however, is substantially more intuitive and convenient. Note also that Currying in ...
5. Functional Programming
... programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a r ...
... programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a r ...
5. Functional Programming
... programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a r ...
... programming language incorporating many recent innovations in programming language design. Haskell provides higher-order functions, non-strict semantics, static polymorphic typing, user-defined algebraic datatypes, pattern-matching, list comprehensions, a module system, a monadic I/O system, and a r ...