Slides
... Implementing Lazy Evaluation How do we implement lazy evaluation? Consider this: datatype 'a stream = ...
... Implementing Lazy Evaluation How do we implement lazy evaluation? Consider this: datatype 'a stream = ...
Lecture 3
... Module level scope (i.e., global variables) Built in scope (i.e., predefined python keywords) A word to the wise - do not name your variables when there is a danger of conflicting with modules your may ...
... Module level scope (i.e., global variables) Built in scope (i.e., predefined python keywords) A word to the wise - do not name your variables when there is a danger of conflicting with modules your may ...
A/x - LAMP | EPFL
... Anonymous functions Parameterisation by functions tends to create many small functions. Sometimes it is cumbersome to have to define the functions using def. A shorter notation makes use of anonymous functions, defined as follows: (x1 : T1 , ..., xn : Tn ) ⇒ E defines a function which maps it ...
... Anonymous functions Parameterisation by functions tends to create many small functions. Sometimes it is cumbersome to have to define the functions using def. A shorter notation makes use of anonymous functions, defined as follows: (x1 : T1 , ..., xn : Tn ) ⇒ E defines a function which maps it ...
Local Normal Forms for First-Order Logic with Applications to
... condition. (For very interesting recent results concerning Hanf’s and Gaifman’s theorems from a different point of view see the papers of Libkin and Dong et al. [Lib97, DLW97].) It is easy to see that the straightforward attempt to replace the isomorphism type of a sphere S in Hanf’s condition by it ...
... condition. (For very interesting recent results concerning Hanf’s and Gaifman’s theorems from a different point of view see the papers of Libkin and Dong et al. [Lib97, DLW97].) It is easy to see that the straightforward attempt to replace the isomorphism type of a sphere S in Hanf’s condition by it ...
pdf
... theory of arithmetic is incomplete”, where a formal theory is viewed as one whose theorems are derivable from an axiom system. For such theories there will always be formulas that are true (for instance, in the standard interpretation of arithmetic) but not theorems of the theories. When it comes to ...
... theory of arithmetic is incomplete”, where a formal theory is viewed as one whose theorems are derivable from an axiom system. For such theories there will always be formulas that are true (for instance, in the standard interpretation of arithmetic) but not theorems of the theories. When it comes to ...
slides - Computer and Information Science
... Truth Tables are Exhaustive • The notion of logical consequence we have defined above is acceptable for a definition of a sound argument, but is not very helpful for checking whether a particular argument is sound or not. • The problem is that we must look at all the possible interpretations of the ...
... Truth Tables are Exhaustive • The notion of logical consequence we have defined above is acceptable for a definition of a sound argument, but is not very helpful for checking whether a particular argument is sound or not. • The problem is that we must look at all the possible interpretations of the ...
characterization of classes of frames in modal language
... futurum est, necesse est futurum esse. In the English edition we read: Whatever has been, necessarily has been. Whatever is, must be. Whatever is to be, of necessity will be. This is that necessity which Aristotle treats of (“de propositionibus singularibus et futuris”), and which seems to destroy a ...
... futurum est, necesse est futurum esse. In the English edition we read: Whatever has been, necessarily has been. Whatever is, must be. Whatever is to be, of necessity will be. This is that necessity which Aristotle treats of (“de propositionibus singularibus et futuris”), and which seems to destroy a ...
Lesson 12
... is often computationally expensive. Notice that even if inference is not complete it is desirable that it is sound. Propositional Logic and Predicate Logic each with Modus Ponens as their inference produce are sound but not complete. We shall see that we need further (sound) rules of inference to ac ...
... is often computationally expensive. Notice that even if inference is not complete it is desirable that it is sound. Propositional Logic and Predicate Logic each with Modus Ponens as their inference produce are sound but not complete. We shall see that we need further (sound) rules of inference to ac ...
+ + 1
... λ-Terms Church designed the λ-calculus as a tool to study the fundamental notion of computable function. He therefore sought to strip away all but the bare essentials. The syntax for λ-terms is accordingly very simple. λ-terms are built from: ...
... λ-Terms Church designed the λ-calculus as a tool to study the fundamental notion of computable function. He therefore sought to strip away all but the bare essentials. The syntax for λ-terms is accordingly very simple. λ-terms are built from: ...
ON A MINIMAL SYSTEM OF ARISTOTLE`S SYLLOGISTIC Introduction
... is not adequate with respect to the intended semantics, being sound but not complete with respect to it. The system, failing to fulfil its intended specification, seems to be interesting for a different reason, namely, it is the smallest system built in the style of Lukasiewicz that includes all the ...
... is not adequate with respect to the intended semantics, being sound but not complete with respect to it. The system, failing to fulfil its intended specification, seems to be interesting for a different reason, namely, it is the smallest system built in the style of Lukasiewicz that includes all the ...
Modus ponens
... concepts in logic it must not be mistaken for a logical law; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the "rule of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof ...
... concepts in logic it must not be mistaken for a logical law; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the "rule of definition" and the "rule of substitution". Modus ponens allows one to eliminate a conditional statement from a logical proof ...
Lambda Calculus Background, λ calculus Models of computation
... otherwise, where z (new name) is not free in E or E' ...
... otherwise, where z (new name) is not free in E or E' ...
Chapter1_Parts2
... the assumption that we assume that the switches, lights, and circuit breakers are ok.! If the system is working correctly (all assumables are true), the observations and the knowledge base are consistent (i.e., satisfiable).! The augmented knowledge base is clearly not consistent if the assumables a ...
... the assumption that we assume that the switches, lights, and circuit breakers are ok.! If the system is working correctly (all assumables are true), the observations and the knowledge base are consistent (i.e., satisfiable).! The augmented knowledge base is clearly not consistent if the assumables a ...
slides
... (Recall notes on logic from Inf 1 - Computation and Logic. Alternatively use on-line references (e.g., Wikipedia).) Grammar of formulas: form ::= atom | ¬form | form ∧ form | form ∨ form | form → form The formulas in our example logic program all have very simple structure. (We shall see later this ...
... (Recall notes on logic from Inf 1 - Computation and Logic. Alternatively use on-line references (e.g., Wikipedia).) Grammar of formulas: form ::= atom | ¬form | form ∧ form | form ∨ form | form → form The formulas in our example logic program all have very simple structure. (We shall see later this ...
( (ϕ ∧ ψ) - EEE Canvas
... this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can deduce ϕ ∧ ψ. ...
... this kind of system, there is an “introduction” rule for each connective and an “elimination” rule for each connective. For instance, the introduction rule for “and” might say: if you can deduce ϕ and if you can deduce ψ, then you can deduce ϕ ∧ ψ. ...
functional prog. in scheme
... apply them to arguments, etc. • We’ll look at how functional programming things are done in Lisp ...
... apply them to arguments, etc. • We’ll look at how functional programming things are done in Lisp ...
Mathematical Logic
... Complexity of deciding logical consequence in Propositional Logic The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-expone ...
... Complexity of deciding logical consequence in Propositional Logic The truth table method is Exponential The problem of determining if a formula A containing n primitive propositions, is a logical consequence of the empty set, i.e., the problem of determining if A is valid, (|= A), takes an n-expone ...
functional form
... parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
... parameter and yields a list of values obtained by applying the given function to each element of a list of parameters ...
fp_in_scheme
... a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • But first, let’s see how to define a general version of compose taking any number of args ...
... a new function that applies f to the result of applying g to x • We’ll look at how the variable environments work to support this in the next topic, closures • But first, let’s see how to define a general version of compose taking any number of args ...
3. Functional Programming
... represented as lists that resemble lambda expressions and are then interpreted or compiled. APL is a language for manipulating arrays and arrays of arrays. Programs are built up of functional operators applied to arrays. Later languages like Mathematica owe a great deal to APL. ISWIM is a paper lang ...
... represented as lists that resemble lambda expressions and are then interpreted or compiled. APL is a language for manipulating arrays and arrays of arrays. Programs are built up of functional operators applied to arrays. Later languages like Mathematica owe a great deal to APL. ISWIM is a paper lang ...
MATH 4110: Advanced Logic
... An excellent student has a clear comprehension of the details of an intricate, non‐trivial mathema cal result: the completeness of first‐order logic with iden ty. They can give a clear and comprehensive outline of the major steps in the proof using their own words and without notes. They have a clea ...
... An excellent student has a clear comprehension of the details of an intricate, non‐trivial mathema cal result: the completeness of first‐order logic with iden ty. They can give a clear and comprehensive outline of the major steps in the proof using their own words and without notes. They have a clea ...
