24,130 research outputs found
Doing and Showing
The persisting gap between the formal and the informal mathematics is due to
an inadequate notion of mathematical theory behind the current formalization
techniques. I mean the (informal) notion of axiomatic theory according to which
a mathematical theory consists of a set of axioms and further theorems deduced
from these axioms according to certain rules of logical inference. Thus the
usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure
Invariant Synthesis for Incomplete Verification Engines
We propose a framework for synthesizing inductive invariants for incomplete
verification engines, which soundly reduce logical problems in undecidable
theories to decidable theories. Our framework is based on the counter-example
guided inductive synthesis principle (CEGIS) and allows verification engines to
communicate non-provability information to guide invariant synthesis. We show
precisely how the verification engine can compute such non-provability
information and how to build effective learning algorithms when invariants are
expressed as Boolean combinations of a fixed set of predicates. Moreover, we
evaluate our framework in two verification settings, one in which verification
engines need to handle quantified formulas and one in which verification
engines have to reason about heap properties expressed in an expressive but
undecidable separation logic. Our experiments show that our invariant synthesis
framework based on non-provability information can both effectively synthesize
inductive invariants and adequately strengthen contracts across a large suite
of programs
Retrieval of episodic versus generic information: Does the order of recall affect the amount and accuracy of details reported by children about repeated events?
Children (N = 157) 4- to 8-years old participated 1 (single) or 4 times (repeated) in an interactive event. Across each condition, half were questioned a week later about the only or a specific occurrence of the event (Depth-first), and then about what usually happens. Half were prompted in the reverse order (Breadth-first). Children with repeated experience who first were asked about what usually happens reported more event-related information overall than those asked about an occurrence first. All children used episodic language when describing an occurrence; however children with repeated-event experience used episodic language less often when describing what usually happens than did those with single experience. Accuracy rates did not differ between conditions. Implications for theories of repeated-event memory are discussed
On ambitious higher-order theories of consciousness
ABSTRACTAmbitious Higher-order theories of consciousness – Higher-order theories that purport to give an account of phenomenal consciousness – face a well-known objection from the possibility of ra..
Higher-order Program Verification as Satisfiability Modulo Theories with Algebraic Data-types
We report on work in progress on automatic procedures for proving properties
of programs written in higher-order functional languages. Our approach encodes
higher-order programs directly as first-order SMT problems over Horn clauses.
It is straight-forward to reduce Hoare-style verification of first-order
programs into satisfiability of Horn clauses. The presence of closures offers
several challenges: relatively complete proof systems have to account for
closures; and in practice, the effectiveness of search procedures depend on
encoding strategies and capabilities of underlying solvers. We here use
algebraic data-types to encode closures and rely on solvers that support
algebraic data-types. The viability of the approach is examined using examples
from the literature on higher-order program verification
An interactive semantics of logic programming
We apply to logic programming some recently emerging ideas from the field of
reduction-based communicating systems, with the aim of giving evidence of the
hidden interactions and the coordination mechanisms that rule the operational
machinery of such a programming paradigm. The semantic framework we have chosen
for presenting our results is tile logic, which has the advantage of allowing a
uniform treatment of goals and observations and of applying abstract
categorical tools for proving the results. As main contributions, we mention
the finitary presentation of abstract unification, and a concurrent and
coordinated abstract semantics consistent with the most common semantics of
logic programming. Moreover, the compositionality of the tile semantics is
guaranteed by standard results, as it reduces to check that the tile systems
associated to logic programs enjoy the tile decomposition property. An
extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory
and Practice of Logic Programmin
Constraint Logic Programming for Natural Language Processing
This paper proposes an evaluation of the adequacy of the constraint logic
programming paradigm for natural language processing. Theoretical aspects of
this question have been discussed in several works. We adopt here a pragmatic
point of view and our argumentation relies on concrete solutions. Using actual
contraints (in the CLP sense) is neither easy nor direct. However, CLP can
improve parsing techniques in several aspects such as concision, control,
efficiency or direct representation of linguistic formalism. This discussion is
illustrated by several examples and the presentation of an HPSG parser.Comment: 15 pages, uuencoded and compressed postscript to appear in
Proceedings of the 5th Int. Workshop on Natural Language Understanding and
Logic Programming. Lisbon, Portugal. 199
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