483 research outputs found
A Lambda Calculus for Quantum Computation
The classical lambda calculus may be regarded both as a programming language
and as a formal algebraic system for reasoning about computation. It provides a
computational model equivalent to the Turing machine, and continues to be of
enormous benefit in the classical theory of computation. We propose that
quantum computation, like its classical counterpart, may benefit from a version
of the lambda calculus suitable for expressing and reasoning about quantum
algorithms. In this paper we develop a quantum lambda calculus as an
alternative model of quantum computation, which combines some of the benefits
of both the quantum Turing machine and the quantum circuit models. The calculus
turns out to be closely related to the linear lambda calculi used in the study
of Linear Logic. We set up a computational model and an equational proof system
for this calculus, and we argue that it is equivalent to the quantum Turing
machine.Comment: To appear in SIAM Journal on Computing. Minor corrections and
improvements. Simulator available at
http://www.het.brown.edu/people/andre/qlambda/index.htm
Formats of Winning Strategies for Six Types of Pushdown Games
The solution of parity games over pushdown graphs (Walukiewicz '96) was the
first step towards an effective theory of infinite-state games. It was shown
that winning strategies for pushdown games can be implemented again as pushdown
automata. We continue this study and investigate the connection between game
presentations and winning strategies in altogether six cases of game arenas,
among them realtime pushdown systems, visibly pushdown systems, and counter
systems. In four cases we show by a uniform proof method that we obtain
strategies implementable by the same type of pushdown machine as given in the
game arena. We prove that for the two remaining cases this correspondence
fails. In the conclusion we address the question of an abstract criterion that
explains the results
Analytic Tableaux for Simple Type Theory and its First-Order Fragment
We study simple type theory with primitive equality (STT) and its first-order
fragment EFO, which restricts equality and quantification to base types but
retains lambda abstraction and higher-order variables. As deductive system we
employ a cut-free tableau calculus. We consider completeness, compactness, and
existence of countable models. We prove these properties for STT with respect
to Henkin models and for EFO with respect to standard models. We also show that
the tableau system yields a decision procedure for three EFO fragments
The History and Prehistory of Natural-Language Semantics
Contemporary natural-language semantics began with the assumption that the meaning of a sentence could be modeled by a single truth condition, or by an entity with a truth-condition. But with the recent explosion of dynamic semantics and pragmatics and of work on non- truth-conditional dimensions of linguistic meaning, we are now in the midst of a shift away from a truth-condition-centric view and toward the idea that a sentence’s meaning must be spelled out in terms of its various roles in conversation. This communicative turn in semantics raises historical questions: Why was truth-conditional semantics dominant in the first place, and why were the phenomena now driving the communicative turn initially ignored or misunderstood by truth-conditional semanticists? I offer a historical answer to both questions. The history of natural-language semantics—springing from the work of Donald Davidson and Richard Montague—began with a methodological toolkit that Frege, Tarski, Carnap, and others had created to better understand artificial languages. For them, the study of linguistic meaning was subservient to other explanatory goals in logic, philosophy, and the foundations of mathematics, and this subservience was reflected in the fact that they idealized away from all aspects of meaning that get in the way of a one-to-one correspondence between sentences and truth-conditions. The truth-conditional beginnings of natural- language semantics are best explained by the fact that, upon turning their attention to the empirical study of natural language, Davidson and Montague adopted the methodological toolkit assembled by Frege, Tarski, and Carnap and, along with it, their idealization away from non-truth-conditional semantic phenomena. But this pivot in explana- tory priorities toward natural language itself rendered the adoption of the truth-conditional idealization inappropriate. Lifting the truth-conditional idealization has forced semanticists to upend the conception of linguistic meaning that was originally embodied in their methodology
Noncomparabilities & Non Standard Logics
Many normative theories set forth in the welfare economics, distributive justice and cognate literatures posit noncomparabilities or incommensurabilities between magnitudes of various kinds. In some cases these gaps are predicated on metaphysical claims, in others upon epistemic claims, and in still others upon political-moral claims. I show that in all such cases they are best given formal expression in nonstandard logics that reject bivalence, excluded middle, or both. I do so by reference to an illustrative case study: a contradiction known to beset John Rawls\u27s selection and characterization of primary goods as the proper distribuendum in any distributively just society. The contradiction is avoided only by reformulating Rawls\u27s claims in a nonstandard form, which form happens also to cohere quite attractively with Rawls\u27s intuitive argumentation on behalf of his claims
Introduction to mathematical logic
Vol. 1, "A revised and much enlarged edition of Introduction to mathematical logic ... which was published in 1944 as one of the Annals of mathematics studies."Mode of access: Internet
Special Cases of the Decision Problem. A Correction
Church Alonzo. Special Cases of the Decision Problem. A Correction. In: Revue Philosophique de Louvain. Troisième série, tome 50, n°26, 1952. pp. 270-272
Special Cases of the Decision Problem. A Correction
Church Alonzo. Special Cases of the Decision Problem. A Correction. In: Revue Philosophique de Louvain. Troisième série, tome 50, n°26, 1952. pp. 270-272
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