5,574 research outputs found
On the definition of the classical connectives and quantifiers
Classical logic is embedded into constructive logic, through a definition of
the classical connectives and quantifiers in terms of the constructive ones.Comment: Why is this a Proof?, Festschrift for Luiz Carlos Pereira , 201
Logicism, Ontology, and the Epistemology of Second-Order Logic
In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms of definability, can serve a neo-logicist's purposes. The problem, in both cases, is similar: neither Wright nor Hale is sufficiently sensitive to the demands that impredicativity imposes. Finally, I defend my own earlier attempt to finesse this issue, in "A Logic for Frege's Theorem", from Hale's criticisms
Naming the largest number: Exploring the boundary between mathematics and the philosophy of mathematics
What is the largest number accessible to the human imagination? The question
is neither entirely mathematical nor entirely philosophical. Mathematical
formulations of the problem fall into two classes: those that fail to fully
capture the spirit of the problem, and those that turn it back into a
philosophical problem
Goal-Driven Query Answering for Existential Rules with Equality
Inspired by the magic sets for Datalog, we present a novel goal-driven
approach for answering queries over terminating existential rules with equality
(aka TGDs and EGDs). Our technique improves the performance of query answering
by pruning the consequences that are not relevant for the query. This is
challenging in our setting because equalities can potentially affect all
predicates in a dataset. We address this problem by combining the existing
singularization technique with two new ingredients: an algorithm for
identifying the rules relevant to a query and a new magic sets algorithm. We
show empirically that our technique can significantly improve the performance
of query answering, and that it can mean the difference between answering a
query in a few seconds or not being able to process the query at all
Encoding TLA+ set theory into many-sorted first-order logic
We present an encoding of Zermelo-Fraenkel set theory into many-sorted
first-order logic, the input language of state-of-the-art SMT solvers. This
translation is the main component of a back-end prover based on SMT solvers in
the TLA+ Proof System
Analyzing Individual Proofs as the Basis of Interoperability between Proof Systems
We describe the first results of a project of analyzing in which theories
formal proofs can be ex- pressed. We use this analysis as the basis of
interoperability between proof systems.Comment: In Proceedings PxTP 2017, arXiv:1712.0089
Some Concerns Regarding Ternary-relation Semantics and Truth-theoretic Semantics in General
This paper deals with a collection of concerns that, over a period of time, led the author away from the Routley–Meyer semantics, and towards proof- theoretic approaches to relevant logics, and indeed to the weak relevant logic MC of meaning containment
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