58,425 research outputs found
Tight Logic Programs
This note is about the relationship between two theories of negation as
failure -- one based on program completion, the other based on stable models,
or answer sets. Francois Fages showed that if a logic program satisfies a
certain syntactic condition, which is now called ``tightness,'' then its stable
models can be characterized as the models of its completion. We extend the
definition of tightness and Fages' theorem to programs with nested expressions
in the bodies of rules, and study tight logic programs containing the
definition of the transitive closure of a predicate.Comment: To appear in Special Issue of the Theory and Practice of Logic
Programming Journal on Answer Set Programming, 200
What's Right With a Syntactic Approach to Theories and Models?
Syntactic approaches in the philosophy of science, which are based on formalizations in predicate logic, are often considered in principle inferior to semantic approaches, which are based on formalizations with the help of structures. To compare the two kinds of approach, I identify some ambiguities in common semantic accounts and explicate the concept of a structure in a way that avoids hidden references to a specific vocabulary. From there, I argue that contrary to common opinion (i) unintended models do not pose a significant problem for syntactic approaches to scientific theories, (ii) syntactic approaches can be at least as language independent as semantic ones, and (iii) in syntactic approaches, scientific theories can be as well connected to the world as in semantic ones. Based on these results, I argue that syntactic and semantic approaches fare equally well when it comes to (iv) ease of application, (iv) accommodating the use of models in the sciences, and (vi) capturing the theory-observation relation
A paradox of syntactic priming: why response tendencies show priming for passives, and response latencies show priming for actives
Speakers tend to repeat syntactic structures across sentences, a phenomenon called syntactic priming. Although it has been suggested that repeating syntactic structures should result in speeded responses, previous research has focused on effects in response tendencies. We investigated syntactic priming effects simultaneously in response tendencies and response latencies for active and passive transitive sentences in a picture description task. In Experiment 1, there were priming effects in response tendencies for passives and in response latencies for actives. However, when participants' pre-existing preference for actives was altered in Experiment 2, syntactic priming occurred for both actives and passives in response tendencies as well as in response latencies. This is the first investigation of the effects of structure frequency on both response tendencies and latencies in syntactic priming. We discuss the implications of these data for current theories of syntactic processing
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com
On the strength of proof-irrelevant type theories
We present a type theory with some proof-irrelevance built into the
conversion rule. We argue that this feature is useful when type theory is used
as the logical formalism underlying a theorem prover. We also show a close
relation with the subset types of the theory of PVS. We show that in these
theories, because of the additional extentionality, the axiom of choice implies
the decidability of equality, that is, almost classical logic. Finally we
describe a simple set-theoretic semantics.Comment: 20 pages, Logical Methods in Computer Science, Long version of IJCAR
2006 pape
On Counterexample Guided Quantifier Instantiation for Synthesis in CVC4
We introduce the first program synthesis engine implemented inside an SMT
solver. We present an approach that extracts solution functions from
unsatisfiability proofs of the negated form of synthesis conjectures. We also
discuss novel counterexample-guided techniques for quantifier instantiation
that we use to make finding such proofs practically feasible. A particularly
important class of specifications are single-invocation properties, for which
we present a dedicated algorithm. To support syntax restrictions on generated
solutions, our approach can transform a solution found without restrictions
into the desired syntactic form. As an alternative, we show how to use
evaluation function axioms to embed syntactic restrictions into constraints
over algebraic datatypes, and then use an algebraic datatype decision procedure
to drive synthesis. Our experimental evaluation on syntax-guided synthesis
benchmarks shows that our implementation in the CVC4 SMT solver is competitive
with state-of-the-art tools for synthesis
Recommended from our members
Erratum to: Experimental syntax and the variation of island effects in English and Italian, Nat Lang Linguist Theory, (2015), 10.1007/s11049-015-9286-8
- …