A Note on Assumptions about Skolem Functions
... An occurrence is a word over IN. Let denote the empty word. Then we define the set of occurrences occ(Φ) of a formula Φ as follows: (i) the empty word is in occ(Φ) (ii) i.π is in occ(Φ) iff Φ = Ψ1 ∧ . . . ∧ Ψn or Φ = Ψ1 ∨ . . . ∨ Ψn , 1 ≤ i ≤ n and π ∈ occ(Ψi ) (iii) 1.π (2.π) is in occ(Φ) iff Φ ...
... An occurrence is a word over IN. Let denote the empty word. Then we define the set of occurrences occ(Φ) of a formula Φ as follows: (i) the empty word is in occ(Φ) (ii) i.π is in occ(Φ) iff Φ = Ψ1 ∧ . . . ∧ Ψn or Φ = Ψ1 ∨ . . . ∨ Ψn , 1 ≤ i ≤ n and π ∈ occ(Ψi ) (iii) 1.π (2.π) is in occ(Φ) iff Φ ...
Lesson 2
... Note: The connectives “because”, “therefore”, “since”, etc. do not correspond to the logical implication! – “The ice-hockey team lost the match, therefore the players came home from the world championship earlier”. “Because I am sick, I stay at home”. – “sick” “home”? But then it would have to be ...
... Note: The connectives “because”, “therefore”, “since”, etc. do not correspond to the logical implication! – “The ice-hockey team lost the match, therefore the players came home from the world championship earlier”. “Because I am sick, I stay at home”. – “sick” “home”? But then it would have to be ...
Relative normalization
... another one) does not say anything about the translation of terms. The reason is that in some cases, it is desirable to interpret a theory with a rich term language (such as Peano arithmetic) into a theory with a poor one (such as set theory), so that we can not expect that terms of T are always int ...
... another one) does not say anything about the translation of terms. The reason is that in some cases, it is desirable to interpret a theory with a rich term language (such as Peano arithmetic) into a theory with a poor one (such as set theory), so that we can not expect that terms of T are always int ...
CSP 506 Comparative Programming Languages
... • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative program ...
... • The basic process of computation is fundamentally different in a FPL than in an imperative language – In an imperative language, operations are done and the results are stored in variables for later use – Management of variables is a constant concern and source of complexity for imperative program ...
Binary Decision Diagrams for First Order Predicate Logic
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
... Proof: The transformation operators can be formulated as rewrite rules.l1 and l2 are ...
presentation - Queaso Systems nv
... Strongly typed programs can’t go wrong • Type inference tries to find the most general type of function o Depending on the functions that are being used ...
... Strongly typed programs can’t go wrong • Type inference tries to find the most general type of function o Depending on the functions that are being used ...
Annotated_Chapter_4_slides
... denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
... denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
Logic: Introduction - Department of information engineering and
... Logic and Computer Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outline of the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
... Logic and Computer Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outline of the Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
(p q r) (p q r) (p q r) (p q r) ( p q r)
... This rule does not lead to an equivalent formula. But it preserves satisfiability. Proof: Let formula (A l) (B l) be non-contradictory. hence there is a valuation v in which it is true. But then in this v both the disjuncts (so called clauses) are true: (A l) and (B l). Let v(l) = 0. The ...
... This rule does not lead to an equivalent formula. But it preserves satisfiability. Proof: Let formula (A l) (B l) be non-contradictory. hence there is a valuation v in which it is true. But then in this v both the disjuncts (so called clauses) are true: (A l) and (B l). Let v(l) = 0. The ...
x - WordPress.com
... In Artificial Intelligence (AI) the ultimate goal is to create machines that think like humans. Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to ...
... In Artificial Intelligence (AI) the ultimate goal is to create machines that think like humans. Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to ...
conditional expressions
... denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
... denoted using the symbol, as in x x+x. In Haskell, the use of the symbol for nameless functions comes from the lambda calculus, the theory of functions on which Haskell is based. ...
conditional expressions
... application has priority over (:). For example, the following definition gives an error: head x:_ = x Hugs> hd [1, 2, 3] where hd x:_ = x ERROR - Syntax error in declaration (unexpected symbol ":") Hugs> hd [1, 2, 3] where hd (x:_) = x ...
... application has priority over (:). For example, the following definition gives an error: head x:_ = x Hugs> hd [1, 2, 3] where hd x:_ = x ERROR - Syntax error in declaration (unexpected symbol ":") Hugs> hd [1, 2, 3] where hd (x:_) = x ...
Lesson 3
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
... Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjunction in which each symbol (element of S) occurs just once: Ex.: p q Disjunctive normal form (DNF) of a formula F is a formula F’ such that F’ is equivalent to F and F’ ha ...
PPT
... • Can write semantics using lambda calculus, extended with operators like modify : (state var value) state ...
... • Can write semantics using lambda calculus, extended with operators like modify : (state var value) state ...
Y in Practical Programs Extended Abstract
... languages as it will not type check. There are two ways around this: either use the programming language’s recursion construct, or (more esoterically) its recursive type construct. In Standard ML [MTHM97], Y is most easily written using fun, the recursive function construct fun Y f x = f (Y f) x Thi ...
... languages as it will not type check. There are two ways around this: either use the programming language’s recursion construct, or (more esoterically) its recursive type construct. In Standard ML [MTHM97], Y is most easily written using fun, the recursive function construct fun Y f x = f (Y f) x Thi ...
LN10
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
... Function type 18.1 The function type a->b (“Haskell is strongly typed” – PDG’s notes, p.7) Objects of type a->b are constructed by lambda abstraction \x->e and used in function application f e’. Lambda abstraction: if e has type b and x is a variable of type a then \x->e has type a->b Function appl ...
Lesson 2
... Note: The connectives “because”, “therefore”, “since”, etc. do not correspond to the logical implication! – “The ice-hockey team lost the match, therefore the players came home from the world championship earlier”. “Because I am sick, I stay at home”. – “sick” “home”? But then it would have to be ...
... Note: The connectives “because”, “therefore”, “since”, etc. do not correspond to the logical implication! – “The ice-hockey team lost the match, therefore the players came home from the world championship earlier”. “Because I am sick, I stay at home”. – “sick” “home”? But then it would have to be ...
Lambda the Ultimate - Rice University Campus Wiki
... “Lambda expressions are especially useful when you want to perform operations on a list or other collection and want to avoid the extra work of defining a function. Many F# library functions take function values as arguments, and it can be especially convenient to use a lambda expression in those ca ...
... “Lambda expressions are especially useful when you want to perform operations on a list or other collection and want to avoid the extra work of defining a function. Many F# library functions take function values as arguments, and it can be especially convenient to use a lambda expression in those ca ...
Natural deduction for predicate logic
... and there are six new rules (introduction and elimination for each of the new features). We will also introduce one derived rule not in the textbook, for convenience. ...
... and there are six new rules (introduction and elimination for each of the new features). We will also introduce one derived rule not in the textbook, for convenience. ...
First-order logic;
... Bottom line: If n is large, then it is almost certain that a random graph will be connected. In fact, with probability approaching 1, all nodes are connected by a path of length at most 2. ...
... Bottom line: If n is large, then it is almost certain that a random graph will be connected. In fact, with probability approaching 1, all nodes are connected by a path of length at most 2. ...