Functional Programming with Relations 1
... size, and build such a grid explicitly using combining forms which stack components beside and above one another. While this approach would allow us to experiment with regular programs, it is far from satisfactory. Having multiple occurrences of the same combining forms and primitive cells would cer ...
... size, and build such a grid explicitly using combining forms which stack components beside and above one another. While this approach would allow us to experiment with regular programs, it is far from satisfactory. Having multiple occurrences of the same combining forms and primitive cells would cer ...
Simple multiplicative proof nets with units
... Here is a passage from Girard’s Proof Nets: the Parallel Syntax for Proof Theory [Gir96, §A.2]1 : There are two multiplicative neutrals, 1 and ⊥, and two rules, the axiom ⊢ 1 and the weakening rule: from ⊢ Γ, deduce ⊢ Γ, ⊥. Both rules are handled by means of links with one conclusion and no premise; ...
... Here is a passage from Girard’s Proof Nets: the Parallel Syntax for Proof Theory [Gir96, §A.2]1 : There are two multiplicative neutrals, 1 and ⊥, and two rules, the axiom ⊢ 1 and the weakening rule: from ⊢ Γ, deduce ⊢ Γ, ⊥. Both rules are handled by means of links with one conclusion and no premise; ...
Partiality and recursion in interactive theorem provers: An overview
... Functional of a Recursive Definition. Given a (recursive) definition f : A → B, we can define a second order function (or functional) F : (A → B) → A → B such that F is itself non-recursive and f = F f . For example, a functional for the addition of natural numbers is the following: F = λh x y. if x ...
... Functional of a Recursive Definition. Given a (recursive) definition f : A → B, we can define a second order function (or functional) F : (A → B) → A → B such that F is itself non-recursive and f = F f . For example, a functional for the addition of natural numbers is the following: F = λh x y. if x ...
Everything is Knowable - Computer Science Intranet
... The AGM framework has been redescribed and expanded in modal logic. In retrospect, one could say that this required three steps. The first step made it possible to have belief revision operators in the logical language, by formalizing these (meta-logical) operations as dynamic modal operators. In th ...
... The AGM framework has been redescribed and expanded in modal logic. In retrospect, one could say that this required three steps. The first step made it possible to have belief revision operators in the logical language, by formalizing these (meta-logical) operations as dynamic modal operators. In th ...
Modeling Data With Functional Programming In R
... features. Many of these concepts originate from the lambda calculus, a mathematical framework for describing computation via functions. While each functional language supports a slightly di↵erent set of features, there is a minimal set of overlapping concepts that we can consider to form the basis o ...
... features. Many of these concepts originate from the lambda calculus, a mathematical framework for describing computation via functions. While each functional language supports a slightly di↵erent set of features, there is a minimal set of overlapping concepts that we can consider to form the basis o ...
Loop Formulas for Circumscription - Joohyung Lee
... One problem is that it is defined for formulas of the form G ⊃ p, rather than for arbitrary formulas. Thus Clark’s completion can be compared with circumscription only when formulas are given in this special form. Moreover, Clark’s completion is sensitive to the syntactic form of the given knowledge ...
... One problem is that it is defined for formulas of the form G ⊃ p, rather than for arbitrary formulas. Thus Clark’s completion can be compared with circumscription only when formulas are given in this special form. Moreover, Clark’s completion is sensitive to the syntactic form of the given knowledge ...
No Syllogisms for the Numerical Syllogistic
... The following questions now arise. Does there exist a finite set X of syllogistic rules in N † such that the direct derivation relation `X is sound and complete? If not, does there at least exist a finite set X of syllogistic rules in N † such that the indirect derivation relation X is sound and co ...
... The following questions now arise. Does there exist a finite set X of syllogistic rules in N † such that the direct derivation relation `X is sound and complete? If not, does there at least exist a finite set X of syllogistic rules in N † such that the indirect derivation relation X is sound and co ...
Getting Started With . . . Haskell for Knowledge Representation
... Examples: [Int] is the type of lists of integers; [Char] is the type of lists of characters, or strings. • By pair- or tuple-formation: if a and b are types, then (a,b) is the type of pairs with an object of type a as their first component, and an object of type b as their second component. If a, b ...
... Examples: [Int] is the type of lists of integers; [Char] is the type of lists of characters, or strings. • By pair- or tuple-formation: if a and b are types, then (a,b) is the type of pairs with an object of type a as their first component, and an object of type b as their second component. If a, b ...
functional form
... architecture of the machines on which programs will run Copyright © 2006 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2006 Addison-Wesley. All rights reserved. ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... as least fixpoint of a logic program, it has been due to an excess of information in the program (possibly erroneous information). As a result, rejecting noncoherent interpretations seems convenient as well. An important remark is that coherence can be interpreted with an empirical sense and that th ...
... as least fixpoint of a logic program, it has been due to an excess of information in the program (possibly erroneous information). As a result, rejecting noncoherent interpretations seems convenient as well. An important remark is that coherence can be interpreted with an empirical sense and that th ...
CSE 20 - Lecture 14: Logic and Proof Techniques
... Check the correctness of a statement: whether a sentence/paragraph/proposition is logically correct. ...
... Check the correctness of a statement: whether a sentence/paragraph/proposition is logically correct. ...
The Dedekind Reals in Abstract Stone Duality
... simply never introduces discontinuous functions. Maps are defined by a (form of) λ-calculus, so we sometimes refer to spaces as types. Statements in the theory are expressed as equations between terms. Since not every formula of (for example) the predicate calculus is of this form, the theory impose ...
... simply never introduces discontinuous functions. Maps are defined by a (form of) λ-calculus, so we sometimes refer to spaces as types. Statements in the theory are expressed as equations between terms. Since not every formula of (for example) the predicate calculus is of this form, the theory impose ...
Proof Search in Modal Logic
... 1.2.1 Formal systems and provability Peano Arithmetic (PA) is a formal system whose axioms are the axioms of classical firstorder logic (including those for falsum), axioms for zero and successor, recursion axioms for addition and multiplication, and the induction axiom scheme. PA’s inference rules ...
... 1.2.1 Formal systems and provability Peano Arithmetic (PA) is a formal system whose axioms are the axioms of classical firstorder logic (including those for falsum), axioms for zero and successor, recursion axioms for addition and multiplication, and the induction axiom scheme. PA’s inference rules ...
logic for computer science - Institute for Computing and Information
... you how to reason about programs - perhaps to show that two apparently different programs are equivalent. Logic is the study of formal (i.e. symbolic) systems of reasoning and of methods of attaching meaning to them. So there are strong parallels between formal computer science and logic. Both invol ...
... you how to reason about programs - perhaps to show that two apparently different programs are equivalent. Logic is the study of formal (i.e. symbolic) systems of reasoning and of methods of attaching meaning to them. So there are strong parallels between formal computer science and logic. Both invol ...
possible-worlds semantics for modal notions conceived as predicates
... to which this kind of reasoning simply does not apply. We do not discuss these arguments here. It is compatible with our account to conceive either as a predicate of sentences or as a predicate of propositions—as long as the latter share the structure of sentences. If we opt for sentences as objec ...
... to which this kind of reasoning simply does not apply. We do not discuss these arguments here. It is compatible with our account to conceive either as a predicate of sentences or as a predicate of propositions—as long as the latter share the structure of sentences. If we opt for sentences as objec ...
COND - Unicauca
... • The objective of the design of a FPL is to mimic mathematical functions to the greatest extent possible • 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 ...
... • The objective of the design of a FPL is to mimic mathematical functions to the greatest extent possible • 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 ...
pdf file
... the semantics of the theory) principle. It applies to all contexts independently on the subject matter, might it be temporal projection, causal relations, frame problem, or any other sort of epistemic situation which requires practical or common sense reasoning. To implement the exceptions-first pri ...
... the semantics of the theory) principle. It applies to all contexts independently on the subject matter, might it be temporal projection, causal relations, frame problem, or any other sort of epistemic situation which requires practical or common sense reasoning. To implement the exceptions-first pri ...
pl9ch15 - Systems and Computer Engineering
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
Chapter 1 - eLisa UGM
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
Chapter 1
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2009 Addison-Wesley. All rights reserved. ...
One-dimensional Fragment of First-order Logic
... logic GNFO. This logic only allows negations of formulae that are guarded in the sense of the guarded fragment. The guarded negation fragment has been shown complete for 2NEXPTIME in [2]. Two-variable logic and guarded-fragment are examples of decidable fragments of first-order logic that are not ba ...
... logic GNFO. This logic only allows negations of formulae that are guarded in the sense of the guarded fragment. The guarded negation fragment has been shown complete for 2NEXPTIME in [2]. Two-variable logic and guarded-fragment are examples of decidable fragments of first-order logic that are not ba ...