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... † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
... † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. ...
Constraint Logic Programming with Hereditary Harrop Formula
... Herbrand universe by providing the ability to program with Horn clauses over different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et a ...
... Herbrand universe by providing the ability to program with Horn clauses over different computation domains, whose logical behaviour is given by constraint systems. CLP languages keep all the good semantic properties of pure logic programming, including soundness and completeness results (Jaffar et a ...
Computational lambda calculus: A combination of functional and
... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...
... Functional programming languages, cf Lisp, have their roots in the lambda calculus and are widely known for their expressive power and simple semantics. Because of their mathematical simplicity are considered to be a great tool for formal analysis and program verification. Functional programs do not ...
A treatise on properly writing mathematical proofs.
... capacity and comfort with formal notation. Susanna Epp’s book divides them into proofs by exhaustion (when the domain is small enough to do them), proofs by “division into cases” (where we partition the domain in non-overlapping parts, which allows us to prove the statement for every sub-domain inde ...
... capacity and comfort with formal notation. Susanna Epp’s book divides them into proofs by exhaustion (when the domain is small enough to do them), proofs by “division into cases” (where we partition the domain in non-overlapping parts, which allows us to prove the statement for every sub-domain inde ...
Version 1.5 - Trent University
... and determine their truth. The real fun lies in the relationship between interpretation of statements, truth, and reasoning. This volume develops the basics of two kinds of formal logical systems, propositional logic and first-order logic. Propositional logic attempts to make precise the relationshi ...
... and determine their truth. The real fun lies in the relationship between interpretation of statements, truth, and reasoning. This volume develops the basics of two kinds of formal logical systems, propositional logic and first-order logic. Propositional logic attempts to make precise the relationshi ...
Divide and congruence applied to eta-bisimulation
... Labelled transition systems can be distinguished from each other by a wide range of semantic equivalences, based on e.g. branching structure or decorated versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we foc ...
... Labelled transition systems can be distinguished from each other by a wide range of semantic equivalences, based on e.g. branching structure or decorated versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we foc ...
A Hoare Logic for Linear Systems - School of Electronic Engineering
... such as positions in space, voltages or rates of flow. These quantities will be represented by elements of vector spaces. For example, in systems like that of Figure 1, the positions, velocities, accelerations and forces might be real-valued functions of time, i.e., members of the set V = T → R, whe ...
... such as positions in space, voltages or rates of flow. These quantities will be represented by elements of vector spaces. For example, in systems like that of Figure 1, the positions, velocities, accelerations and forces might be real-valued functions of time, i.e., members of the set V = T → R, whe ...
Integrating Logical Reasoning and Probabilistic Chain Graphs
... where the predicates of the atoms D and Bi are at least unary and the atoms Rj , called templates, express relationships among variables, where at least one variable appearing in the atoms D and Bi occurs in at least one template Rj . An example illustrating this representation is shown below (Examp ...
... where the predicates of the atoms D and Bi are at least unary and the atoms Rj , called templates, express relationships among variables, where at least one variable appearing in the atoms D and Bi occurs in at least one template Rj . An example illustrating this representation is shown below (Examp ...
Introduction
... two wires both “1” - make another be “1” (AND) at least one of two wires “1” - make another be “1” (OR) a wire “1” - then make another be “0” (NOT) Memory devices (store) ...
... two wires both “1” - make another be “1” (AND) at least one of two wires “1” - make another be “1” (OR) a wire “1” - then make another be “0” (NOT) Memory devices (store) ...
pptx
... int oldx; int x = 50; while (x > 0) do { if copied then assert (x <_{T_i} oldx) else if * then { copied=true; oldx=x; ...
... int oldx; int x = 50; while (x > 0) do { if copied then assert (x <_{T_i} oldx) else if * then { copied=true; oldx=x; ...
page 135 ADAPTIVE LOGICS FOR QUESTION EVOCATION
... (ii) for every A ∈ dQ, Γ 6|= A. In the rest of this paper, I shall only consider the evocation of regular questions. 3. Why the Reconstruction is Important It is easily observed that question evocation is a non-monotonic notion: questions evoked by some set of declarative sentences may be suppressed ...
... (ii) for every A ∈ dQ, Γ 6|= A. In the rest of this paper, I shall only consider the evocation of regular questions. 3. Why the Reconstruction is Important It is easily observed that question evocation is a non-monotonic notion: questions evoked by some set of declarative sentences may be suppressed ...
Digital Systems Design 2
... For a moderately complex function, a ROM-based circuit is usually faster than a circuit using multiple SSI/MSI devices and PLDs, and often faster than an FPGA or custom LSI chip in a comparable technology. The program that generates the ROM contents can easily be structured to handle unusual or unde ...
... For a moderately complex function, a ROM-based circuit is usually faster than a circuit using multiple SSI/MSI devices and PLDs, and often faster than an FPGA or custom LSI chip in a comparable technology. The program that generates the ROM contents can easily be structured to handle unusual or unde ...
pdf
... rooted at [>'] contained in'M' such that for all the frontier nodes t of N, qeL'(t) (resp. and for all interior nodes u of N, peL'(u)). Proof. We give the proof for AFq. The proof for A(p U q) is similar. We first assume that in the original structure M, each node has a finite number of successors. ...
... rooted at [>'] contained in'M' such that for all the frontier nodes t of N, qeL'(t) (resp. and for all interior nodes u of N, peL'(u)). Proof. We give the proof for AFq. The proof for A(p U q) is similar. We first assume that in the original structure M, each node has a finite number of successors. ...
- Free Documents
... theory T axiomatized by m p for each m, on the other. The sets p and T are the same, consisting of all nodes that together with all their successors force p, but clearly the theories are not p is not a consequence of T . Similarly, the theory T m p p for each m can be shown to have the strong disjun ...
... theory T axiomatized by m p for each m, on the other. The sets p and T are the same, consisting of all nodes that together with all their successors force p, but clearly the theories are not p is not a consequence of T . Similarly, the theory T m p p for each m can be shown to have the strong disjun ...
477_55789_Session 4
... Logic gates are electronic circuits that can be used to implement the most elementary logic expressions, also known as Boolean expressions. The logic gate is the most basic building block of combinational logic. There are three basic logic gates, namely the OR gate, the AND gate and the NOT gate. Ot ...
... Logic gates are electronic circuits that can be used to implement the most elementary logic expressions, also known as Boolean expressions. The logic gate is the most basic building block of combinational logic. There are three basic logic gates, namely the OR gate, the AND gate and the NOT gate. Ot ...
A Crevice on the Crane Beach: Finite-Degree
... logics are quite far from full FO[ARB], and in that sense, fail A different take originated from a conjecture of Lautemann to identify the part of the arbitrary numerical predicates that and Thérien, investigated by Barrington et al. [10]: the Crane fit the intuition that they are rendered useless b ...
... logics are quite far from full FO[ARB], and in that sense, fail A different take originated from a conjecture of Lautemann to identify the part of the arbitrary numerical predicates that and Thérien, investigated by Barrington et al. [10]: the Crane fit the intuition that they are rendered useless b ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.