Propositional Logic - Department of Computer Science
... If all sequences of rule applications lead to an “obviously unsatisfiable” constraint, then P is unsatisfiable. If at least one sequence of rule applications leads to a constraint that cannot be decomposed further and does not contain an obviously unsatisfiable set of constraints, then P is satisfia ...
... If all sequences of rule applications lead to an “obviously unsatisfiable” constraint, then P is unsatisfiable. If at least one sequence of rule applications leads to a constraint that cannot be decomposed further and does not contain an obviously unsatisfiable set of constraints, then P is satisfia ...
Methods and Patterns for User-friendly Quantum Programming
... expect a QPL to fulfil. These vary accordingly to the underlying paradigm, with frequent requirements amongst others being: completeness, extensibility, abstracting away and being independent from the underlying machinery, and being expressive enough to allow one to define quantum data structures, o ...
... expect a QPL to fulfil. These vary accordingly to the underlying paradigm, with frequent requirements amongst others being: completeness, extensibility, abstracting away and being independent from the underlying machinery, and being expressive enough to allow one to define quantum data structures, o ...
curried functions - Universitatea "Politehnica"
... f maps the empty list to some value v and any non-empty list to some function op applied to its head and f of its tail ...
... f maps the empty list to some value v and any non-empty list to some function op applied to its head and f of its tail ...
Temporal Here and There - Computational Cognition Lab
... In [10], Michael Gelfond and Vladimir Lifschitz introduced the so-called 0 semantics that subsumed many of the existing Logic Programming alternatives but without the syntactic restrictions made by previous approaches. The modelbased orientation of this semantics led to a paradigm suitable for const ...
... In [10], Michael Gelfond and Vladimir Lifschitz introduced the so-called 0 semantics that subsumed many of the existing Logic Programming alternatives but without the syntactic restrictions made by previous approaches. The modelbased orientation of this semantics led to a paradigm suitable for const ...
Beyond Quantifier-Free Interpolation in Extensions of Presburger
... uninterpreted functions (UF), this allows us to encode the theory of extensional arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based ...
... uninterpreted functions (UF), this allows us to encode the theory of extensional arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based ...
Audio Processing using Haskell
... Imperative programming languages are the usual choice for today’s software. The currently popular CPUs conform to the imperative programming paradigm and allow a fast execution of imperative programs. Nevertheless fnctional programming languages like Haskell [1, 2] became valuable alternatives in th ...
... Imperative programming languages are the usual choice for today’s software. The currently popular CPUs conform to the imperative programming paradigm and allow a fast execution of imperative programs. Nevertheless fnctional programming languages like Haskell [1, 2] became valuable alternatives in th ...
Equality in the Presence of Apartness: An Application of Structural
... may require that a and b are computed to infinite precision. If a and b are positively distinct, instead, a finite computation is sufficient. Thus, Brouwer introduced the notion of apartness as a positive, intuitionistic basic concept. He also introduced special notations and terminology for the new int ...
... may require that a and b are computed to infinite precision. If a and b are positively distinct, instead, a finite computation is sufficient. Thus, Brouwer introduced the notion of apartness as a positive, intuitionistic basic concept. He also introduced special notations and terminology for the new int ...
Chapter 15 slides - University of Hawaii
... architecture of the machines on which programs will run Copyright © 2007 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2007 Addison-Wesley. All rights reserved. ...
Nonmonotonic Reasoning - Computer Science Department
... context for applicability of rules. That is all the formulas in T can be reconstructed from W using underlying logic and those rules of D which are not blocked by T . ...
... context for applicability of rules. That is all the formulas in T can be reconstructed from W using underlying logic and those rules of D which are not blocked by T . ...
Show
... subject: “You and love are still my argument” (Shakespeare). 4. Logic. The minor premise in a syllogism. 5. Mathematics. a. The independent variable of a function. b. The amplitude of a ...
... subject: “You and love are still my argument” (Shakespeare). 4. Logic. The minor premise in a syllogism. 5. Mathematics. a. The independent variable of a function. b. The amplitude of a ...
4 The semantics of full first
... terms of L∗C and L∗=,C are—let us retroactively specify—the variables and constants. Variables and constants are the atomic terms of a language. The new ingredients of L# C are the complex terms given by clause (2) above. (b) Proof by induction on length works for terms as well as for formulas. In p ...
... terms of L∗C and L∗=,C are—let us retroactively specify—the variables and constants. Variables and constants are the atomic terms of a language. The new ingredients of L# C are the complex terms given by clause (2) above. (b) Proof by induction on length works for terms as well as for formulas. In p ...
page 3 A CONVERSE BARCAN FORMULA IN ARISTOTLE`S
... First then take a universal negative with the terms a and b. Now if a belongs to no b, b will not belong to any a; for if it, b, does belong to some a (say to c), it will not be true that a belongs to no b — for c is one of the bs (An pr. I.2, 25a14–17).6 It is the cryptic second sentence that sketc ...
... First then take a universal negative with the terms a and b. Now if a belongs to no b, b will not belong to any a; for if it, b, does belong to some a (say to c), it will not be true that a belongs to no b — for c is one of the bs (An pr. I.2, 25a14–17).6 It is the cryptic second sentence that sketc ...
The Taming of the (X)OR
... we apply boolean reduction rules, one can eliminate duplicated literals in a clause, and hence the length of each clause never exceeds the number of available atoms. These two rules, together with a deletion strategy, describe a Gauss-Elimination procedure as known from high-school which has a quadr ...
... we apply boolean reduction rules, one can eliminate duplicated literals in a clause, and hence the length of each clause never exceeds the number of available atoms. These two rules, together with a deletion strategy, describe a Gauss-Elimination procedure as known from high-school which has a quadr ...
Subset Types and Partial Functions
... where x is of type ι. This is to be contrasted with constructive type theories like that of [15], where to type an application of car, that function would have to be applied to an inclusion i(x), not just x. This inclusion will only be typable if cons? x is provable, but that is not the case here. ...
... where x is of type ι. This is to be contrasted with constructive type theories like that of [15], where to type an application of car, that function would have to be applied to an inclusion i(x), not just x. This inclusion will only be typable if cons? x is provable, but that is not the case here. ...
1 Salient Features of Functional Programming
... • No: What if i = j? • This makes code correctness reasoning (by man or machine) even harder: – It is not enough to look at a piece of code by itself. – Instead, the reasoning must be over all states in which it might be executed — and it is easy to miss some cases because the code does not show th ...
... • No: What if i = j? • This makes code correctness reasoning (by man or machine) even harder: – It is not enough to look at a piece of code by itself. – Instead, the reasoning must be over all states in which it might be executed — and it is easy to miss some cases because the code does not show th ...
Query Answering for OWL-DL with Rules
... some of the expressive power of OWL-DL: they are restricted to universal quantification and lack negation in their basic form. To overcome the limitations of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the ...
... some of the expressive power of OWL-DL: they are restricted to universal quantification and lack negation in their basic form. To overcome the limitations of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the ...
From Syllogism to Common Sense Normal Modal Logic
... ‣ Informally, a rule of inference A/B is derivable in a logic L if there is an L -proof of B from A. ‣ If there is an L -proof of B from A, by the rule of substitution there also is an L -proof of #(B) from #(A), for any substitution #. For admissible rules this has to be made explicit. ‣ A rule A/B ...
... ‣ Informally, a rule of inference A/B is derivable in a logic L if there is an L -proof of B from A. ‣ If there is an L -proof of B from A, by the rule of substitution there also is an L -proof of #(B) from #(A), for any substitution #. For admissible rules this has to be made explicit. ‣ A rule A/B ...
Let ав бд гжеиз © § § § § "! be a Boolean algebra, where ¥ for some
... The necessity of the last condition was observed by McKinsey in [12]. Our result shows that this condition is also sufficient and this, it is actually a characterization of Boolean functions. ...
... The necessity of the last condition was observed by McKinsey in [12]. Our result shows that this condition is also sufficient and this, it is actually a characterization of Boolean functions. ...
pdf
... tuples built on the sets s1 , . . . , sn . If x ∈ s1 × . . . × sn , then x = hx1 , . . . , xn i such that xi ∈ si for all i ∈ {1, . . . , n}. ...
... tuples built on the sets s1 , . . . , sn . If x ∈ s1 × . . . × sn , then x = hx1 , . . . , xn i such that xi ∈ si for all i ∈ {1, . . . , n}. ...
G - Courses
... obtained from Herbrand structures via taking the equivalence classes of terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to ...
... obtained from Herbrand structures via taking the equivalence classes of terms according to the equalities between them in some structure satisfying the FO-sentence at hand. Here, we used the resolution procedure only for formulas of propositional logic. The resolution procedure can be extended to ...