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Expressibility of Higher Order Logics
Electronic Notes in Theoretical Computer Science, 2003 AbstractWe study the expressive power of higher order logics on finite relational structures or databases. First, we give a characterization of the expressive power of the fragments Σij and πij, for each order i ≥ 2 and each number of alternations of quantifier blocks j. Then we get as a corollary the expressive power of HOi for each order i ≥ 2.
Lauri Hella, Jose Maria Turull Torres
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Topological Completeness for Higher-Order Logic [PDF]
BRICS Report Series, 1997 Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces - so-called "topological semantics". The first is classical higher order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with ...
Steven Awodey, Carsten Butz
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Semantics of Separation-Logic Typing and Higher-order Frame Rules for Algol-like Languages [PDF]
Logical Methods in Computer Science, 2006 We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables).
Lars Birkedal +2 more
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The Case Against Higher-Order Metaphysics
Metaphysics, 2022 Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order ...
Thomas Hofweber
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Light Logics and Higher-Order Processes [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 We show that the techniques for resource control that have been developed by the so-calledlight logicscan be fruitfully applied also to process algebras. In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time.
DAL LAGO, UGO +2 more
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A second order logic of existence [PDF]
, 1969 Publisher's, offprint versionA. N. Prior in [9] has suggested an approach towards a second order logic of existence where, following medieval logicians, we distinguish “between predicates (like ‘is red’, ‘is hard’, etc.) which entail existence, and ...
Cocchiarella, Nino
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Log-Linear-Based Logic Mining with Multi-Discrete Hopfield Neural Network
Mathematics, 2023 Choosing the best attribute from a dataset is a crucial step in effective logic mining since it has the greatest impact on improving the performance of the induced logic.
Gaeithry Manoharam +6 more
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Higher-Order Logic and Disquotational Truth
Journal of Philosophical Logic, 2022 AbstractTruth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting.
Lavinia María Picollo +1 more
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CIFOL: Case-intensional first order logic. (I) Toward a theory of sorts [PDF]
, 2012 This is Part I of a two-part essay introducing case-intensional first-order logic (CIFOL), an easy-to-use, uniform, powerful, and useful combination of first order logic with modal logic resulting from philosophical and technical modifications of Bressan’
Nuel Belnap +3 more
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Executing Higher Order Logic [PDF]
, 2002 We report on the design of a prototyping component for the theorem prover Isabelle/HOL. Specifications consisting of datatypes, recursive functions and inductive definitions are compiled into a functional program. Functions and inductively defined relations can be mixed.
Stefan Berghofer, Tobias Nipkow
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