On Weak Ground
... condition is stated in terms of sequents with an arbitrary set of sentences φ0 , φ1 , ... on the left-hand side. ...
... condition is stated in terms of sequents with an arbitrary set of sentences φ0 , φ1 , ... on the left-hand side. ...
Hilbert`s Program Then and Now - Philsci
... In about 1920, Hilbert came to reject Russell’s logicist solution to the consistency problem for arithmetic, mainly for the reason that the axiom of reducibility cannot be accepted as a purely logical axiom. In lectures from the Summer term 1920, he concluded that “the aim of reducing set theory, an ...
... In about 1920, Hilbert came to reject Russell’s logicist solution to the consistency problem for arithmetic, mainly for the reason that the axiom of reducibility cannot be accepted as a purely logical axiom. In lectures from the Summer term 1920, he concluded that “the aim of reducing set theory, an ...
Forking in simple theories and CM-triviality Daniel Palacín Cruz
... In chapters 4 and 5 we work inside the second level of the non ample hierarchy, and in chapter 2 we will present two generalizations of the ample hierarchy which are relative to a given ∅-invariant family of partial types. An application of these generalizations is exhibited later in chapter 3. This ...
... In chapters 4 and 5 we work inside the second level of the non ample hierarchy, and in chapter 2 we will present two generalizations of the ample hierarchy which are relative to a given ∅-invariant family of partial types. An application of these generalizations is exhibited later in chapter 3. This ...
Logic in Nonmonotonic Reasoning
... scientific methodology in this sense. The way of thinking in partially known circumstances suggested by nonmonotonic reasoning consists in using reasonable assumptions that can guide us in our decisions. Accordingly, nonmonotonic reasoning can be described as a theory of making and selecting assumpt ...
... scientific methodology in this sense. The way of thinking in partially known circumstances suggested by nonmonotonic reasoning consists in using reasonable assumptions that can guide us in our decisions. Accordingly, nonmonotonic reasoning can be described as a theory of making and selecting assumpt ...
Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011
... least r; similarly, Mra φ states that the rate is at most r. In this respect, our logic is similar to the Aumann’s system [Aum99b] developed for Harsanyi type spaces [Har67]. In spite of their syntactic similarities, CML and PML are very different. In the probabilistic case axiomatized by Zhou in hi ...
... least r; similarly, Mra φ states that the rate is at most r. In this respect, our logic is similar to the Aumann’s system [Aum99b] developed for Harsanyi type spaces [Har67]. In spite of their syntactic similarities, CML and PML are very different. In the probabilistic case axiomatized by Zhou in hi ...
Interpretability formalized
... elementary syntax in arithmetic ([Göd31]) to show the incompleteness of, for example, Peano arithmetic. Interpretations have also been used in partial realizations of Hilbert’s programme and other attempts to settle foundational questions ([Sim88], [Fef88], [Nel86]). For another occurrence of inter ...
... elementary syntax in arithmetic ([Göd31]) to show the incompleteness of, for example, Peano arithmetic. Interpretations have also been used in partial realizations of Hilbert’s programme and other attempts to settle foundational questions ([Sim88], [Fef88], [Nel86]). For another occurrence of inter ...
Making Abstract Domains Condensing
... many authors (see e.g. [Codish and Lagoon 2000; Debray 1994; Jacobs and Langen 1992; King and Lu 2002; Langen 1991; Giacobazzi and Scozzari 1998; Marriott and Søndergaard 1993; Schachte 2003]. Langen [1991] first gave a specific solution to this problem by introducing the idea of so-called condensin ...
... many authors (see e.g. [Codish and Lagoon 2000; Debray 1994; Jacobs and Langen 1992; King and Lu 2002; Langen 1991; Giacobazzi and Scozzari 1998; Marriott and Søndergaard 1993; Schachte 2003]. Langen [1991] first gave a specific solution to this problem by introducing the idea of so-called condensin ...
Lecture 20
... When VIN changes to logic 1, transistor gets cutoff. ID goes to 0. Resistor voltage goes to zero. VOUT “pulled down” to 0 V. ...
... When VIN changes to logic 1, transistor gets cutoff. ID goes to 0. Resistor voltage goes to zero. VOUT “pulled down” to 0 V. ...
Full Text - Institute for Logic, Language and Computation
... decades later. In fact, Ramsey3 proposes a thought experiment to judge the truth-value of a conditional. Technically, the use of the Bayesian conception of probability enables us to give a formal apparatus to this conception. Just after the Second World War, the field became autonomous with Goodman ...
... decades later. In fact, Ramsey3 proposes a thought experiment to judge the truth-value of a conditional. Technically, the use of the Bayesian conception of probability enables us to give a formal apparatus to this conception. Just after the Second World War, the field became autonomous with Goodman ...
The Premiss-Based Approach to Logical Aggregation Franz Dietrich & Philippe Mongin
... formulas, for instance, but not necessarily, by majority voting. By contrast, if ' represents a non-premiss, the decision on ' will typically take into account those made on other formulas; for instance, though again not necessarily, ' or its negate :' logically follows from the accepted premisses. ...
... formulas, for instance, but not necessarily, by majority voting. By contrast, if ' represents a non-premiss, the decision on ' will typically take into account those made on other formulas; for instance, though again not necessarily, ' or its negate :' logically follows from the accepted premisses. ...
A Unified View of Induction Reasoning for First-Order Logic
... studies have been conducted to reduce the gap between them. Protzen [42] proposed a proof strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a method that extends schemata-based induction to deal with a special class of mutually defined fun ...
... studies have been conducted to reduce the gap between them. Protzen [42] proposed a proof strategy to perform lazy induction on particular explicit induction proofs. Kapur and Subramaniam [29] devised a method that extends schemata-based induction to deal with a special class of mutually defined fun ...
PDF - University of Kent
... The Laws of Form (LoF) were developed by George Spencer-Brown (1972) as a way of representing graphically the laws of logic, and in particular the propositional calculus or Boolean algebra. They provide an extremely elegant and parsimonious form of representation for both the algebra and the arithme ...
... The Laws of Form (LoF) were developed by George Spencer-Brown (1972) as a way of representing graphically the laws of logic, and in particular the propositional calculus or Boolean algebra. They provide an extremely elegant and parsimonious form of representation for both the algebra and the arithme ...
IOSR Journal of VLSI and Signal Processing (IOSR-JVSP)
... multiplier plays important roll. In case of digital system performance is generally evaluated by the performance of the multiplier . Many researchers with advances in technology, have tried to design multipliers which offer high speed, low power consumption, regularity of layout. Arithmetic processo ...
... multiplier plays important roll. In case of digital system performance is generally evaluated by the performance of the multiplier . Many researchers with advances in technology, have tried to design multipliers which offer high speed, low power consumption, regularity of layout. Arithmetic processo ...
word - Rackcdn.com
... Dynamic circuits have achieved widespread use because they require less silicon area and have superior performance over conventional static circuits. Unlike static circuits, dynamic circuits store data in the form of charge that dissipates in a short period of time due to leakage current. Consequent ...
... Dynamic circuits have achieved widespread use because they require less silicon area and have superior performance over conventional static circuits. Unlike static circuits, dynamic circuits store data in the form of charge that dissipates in a short period of time due to leakage current. Consequent ...
Elements of Finite Model Theory
... The main sources of motivational examples for finite model theory are found in database theory, computational complexity, and formal languages, although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of ...
... The main sources of motivational examples for finite model theory are found in database theory, computational complexity, and formal languages, although in recent years connections with other areas, such as formal methods and verification, and artificial intelligence, have been discovered. The birth of ...
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.