129,603 research outputs found
A Relational Logic for Higher-Order Programs
Relational program verification is a variant of program verification where
one can reason about two programs and as a special case about two executions of
a single program on different inputs. Relational program verification can be
used for reasoning about a broad range of properties, including equivalence and
refinement, and specialized notions such as continuity, information flow
security or relative cost. In a higher-order setting, relational program
verification can be achieved using relational refinement type systems, a form
of refinement types where assertions have a relational interpretation.
Relational refinement type systems excel at relating structurally equivalent
terms but provide limited support for relating terms with very different
structures.
We present a logic, called Relational Higher Order Logic (RHOL), for proving
relational properties of a simply typed -calculus with inductive types
and recursive definitions. RHOL retains the type-directed flavour of relational
refinement type systems but achieves greater expressivity through rules which
simultaneously reason about the two terms as well as rules which only
contemplate one of the two terms. We show that RHOL has strong foundations, by
proving an equivalence with higher-order logic (HOL), and leverage this
equivalence to derive key meta-theoretical properties: subject reduction,
admissibility of a transitivity rule and set-theoretical soundness. Moreover,
we define sound embeddings for several existing relational type systems such as
relational refinement types and type systems for dependency analysis and
relative cost, and we verify examples that were out of reach of prior work.Comment: Submitted to ICFP 201
Neuro-Symbolic Recommendation Model based on Logic Query
A recommendation system assists users in finding items that are relevant to
them. Existing recommendation models are primarily based on predicting
relationships between users and items and use complex matching models or
incorporate extensive external information to capture association patterns in
data. However, recommendation is not only a problem of inductive statistics
using data; it is also a cognitive task of reasoning decisions based on
knowledge extracted from information. Hence, a logic system could naturally be
incorporated for the reasoning in a recommendation task. However, although
hard-rule approaches based on logic systems can provide powerful reasoning
ability, they struggle to cope with inconsistent and incomplete knowledge in
real-world tasks, especially for complex tasks such as recommendation.
Therefore, in this paper, we propose a neuro-symbolic recommendation model,
which transforms the user history interactions into a logic expression and then
transforms the recommendation prediction into a query task based on this logic
expression. The logic expressions are then computed based on the modular logic
operations of the neural network. We also construct an implicit logic encoder
to reasonably reduce the complexity of the logic computation. Finally, a user's
interest items can be queried in the vector space based on the computation
results. Experiments on three well-known datasets verified that our method
performs better compared to state of the art shallow, deep, session, and
reasoning models.Comment: 17 pages, 6 figure
Neural-Symbolic Recommendation with Graph-Enhanced Information
The recommendation system is not only a problem of inductive statistics from
data but also a cognitive task that requires reasoning ability. The most
advanced graph neural networks have been widely used in recommendation systems
because they can capture implicit structured information from graph-structured
data. However, like most neural network algorithms, they only learn matching
patterns from a perception perspective. Some researchers use user behavior for
logic reasoning to achieve recommendation prediction from the perspective of
cognitive reasoning, but this kind of reasoning is a local one and ignores
implicit information on a global scale. In this work, we combine the advantages
of graph neural networks and propositional logic operations to construct a
neuro-symbolic recommendation model with both global implicit reasoning ability
and local explicit logic reasoning ability. We first build an item-item graph
based on the principle of adjacent interaction and use graph neural networks to
capture implicit information in global data. Then we transform user behavior
into propositional logic expressions to achieve recommendations from the
perspective of cognitive reasoning. Extensive experiments on five public
datasets show that our proposed model outperforms several state-of-the-art
methods, source code is avaliable at [https://github.com/hanzo2020/GNNLR].Comment: 12 pages, 2 figures, conferenc
The Problem of Analogical Inference in Inductive Logic
We consider one problem that was largely left open by Rudolf Carnap in his
work on inductive logic, the problem of analogical inference. After discussing
some previous attempts to solve this problem, we propose a new solution that is
based on the ideas of Bruno de Finetti on probabilistic symmetries. We explain
how our new inductive logic can be developed within the Carnapian paradigm of
inductive logic-deriving an inductive rule from a set of simple postulates
about the observational process-and discuss some of its properties.Comment: In Proceedings TARK 2015, arXiv:1606.0729
Application of aboutness to functional benchmarking in information retrieval
Experimental approaches are widely employed to benchmark the performance of an information retrieval (IR) system. Measurements in terms of recall and precision are computed as performance indicators. Although they are good at assessing the retrieval effectiveness of an IR system, they fail to explore deeper aspects such as its underlying functionality and explain why the system shows such performance. Recently, inductive (i.e., theoretical) evaluation of IR systems has been proposed to circumvent the controversies of the experimental methods. Several studies have adopted the inductive approach, but they mostly focus on theoretical modeling of IR properties by using some metalogic. In this article, we propose to use inductive evaluation for functional benchmarking of IR models as a complement of the traditional experiment-based performance benchmarking. We define a functional benchmark suite in two stages: the evaluation criteria based on the notion of "aboutness," and the formal evaluation methodology using the criteria. The proposed benchmark has been successfully applied to evaluate various well-known classical and logic-based IR models. The functional benchmarking results allow us to compare and analyze the functionality of the different IR models
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