676 research outputs found
On first-order expressibility of satisfiability in submodels
Let be regular cardinals, , let
be a sentence of the language in a given
signature, and let express the fact that holds
in a submodel, i.e., any model in the signature satisfies
if and only if some submodel of satisfies . It was shown in [1] that, whenever is in
in the signature having less than
functional symbols (and arbitrarily many predicate symbols), then
is equivalent to a monadic existential sentence in the
second-order language , and that for any
signature having at least one binary predicate symbol there exists in
such that is not equivalent
to any (first-order) sentence in . Nevertheless, in
certain cases are first-order expressible. In this note,
we provide several (syntactical and semantical) characterizations of the case
when is in and is
or a certain large cardinal
RelBAC: Relation Based Access Control
TheWeb 2.0, GRID applications and, more recently, semantic desktop applications are bringing the Web to a situation where more and more data and metadata are shared and made available to large user groups. In this context, metadata may be tags or complex graph structures such as file system or web directories, or (lightweight) ontologies. In turn, users can themselves be tagged by certain properties, and can be organized in complex directory structures, very much in the same way as data. Things are further complicated by the highly unpredictable and autonomous dynamics of data, users, permissions and access control rules. In this paper we propose a new access control model and a logic, called RelBAC (for Relation Based Access Control) which allows us to deal with this novel scenario. The key idea, which differentiates RelBAC from the state of the art, e.g., Role Based Access Control (RBAC), is that permissions are modeled as relations between users and data, while access control rules are their instantiations on specific sets of users and objects. As such, access control rules are assigned an arity which allows a fine tuning of which users can access which data, and can evolve independently, according to the desires of the policy manager(s). Furthermore, the formalization of the RelBAC model as an Entity-Relationship (ER) model allows for its direct translation into Description Logics (DL). In turn, this allows us to reason, possibly at run time, about access control policies
Modality and expressibility
When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories
Monotonicity and Persistence in Preferential Logics
An important characteristic of many logics for Artificial Intelligence is
their nonmonotonicity. This means that adding a formula to the premises can
invalidate some of the consequences. There may, however, exist formulae that
can always be safely added to the premises without destroying any of the
consequences: we say they respect monotonicity. Also, there may be formulae
that, when they are a consequence, can not be invalidated when adding any
formula to the premises: we call them conservative. We study these two classes
of formulae for preferential logics, and show that they are closely linked to
the formulae whose truth-value is preserved along the (preferential) ordering.
We will consider some preferential logics for illustration, and prove syntactic
characterization results for them. The results in this paper may improve the
efficiency of theorem provers for preferential logics.Comment: See http://www.jair.org/ for any accompanying file
LLM-FuncMapper: Function Identification for Interpreting Complex Clauses in Building Codes via LLM
As a vital stage of automated rule checking (ARC), rule interpretation of
regulatory texts requires considerable effort. However, interpreting regulatory
clauses with implicit properties or complex computational logic is still
challenging due to the lack of domain knowledge and limited expressibility of
conventional logic representations. Thus, LLM-FuncMapper, an approach to
identifying predefined functions needed to interpret various regulatory clauses
based on the large language model (LLM), is proposed. First, by systematically
analysis of building codes, a series of atomic functions are defined to capture
shared computational logics of implicit properties and complex constraints,
creating a database of common blocks for interpreting regulatory clauses. Then,
a prompt template with the chain of thought is developed and further enhanced
with a classification-based tuning strategy, to enable common LLMs for
effective function identification. Finally, the proposed approach is validated
with statistical analysis, experiments, and proof of concept. Statistical
analysis reveals a long-tail distribution and high expressibility of the
developed function database, with which almost 100% of computer-processible
clauses can be interpreted and represented as computer-executable codes.
Experiments show that LLM-FuncMapper achieve promising results in identifying
relevant predefined functions for rule interpretation. Further proof of concept
in automated rule interpretation also demonstrates the possibility of
LLM-FuncMapper in interpreting complex regulatory clauses. To the best of our
knowledge, this study is the first attempt to introduce LLM for understanding
and interpreting complex regulatory clauses, which may shed light on further
adoption of LLM in the construction domain
Tarski's influence on computer science
The influence of Alfred Tarski on computer science was indirect but
significant in a number of directions and was in certain respects fundamental.
Here surveyed is the work of Tarski on the decision procedure for algebra and
geometry, the method of elimination of quantifiers, the semantics of formal
languages, modeltheoretic preservation theorems, and algebraic logic; various
connections of each with computer science are taken up
Craig Interpolation for Decidable First-Order Fragments
We show that the guarded-negation fragment (GNFO) is, in a precise sense, the
smallest extension of the guarded fragment (GFO) with Craig interpolation. In
contrast, we show that the smallest extension of the two-variable fragment
(FO2), and of the forward fragment (FF) with Craig interpolation, is full
first-order logic. Similarly, we also show that all extensions of FO2 and of
the fluted fragment (FL) with Craig interpolation are undecidable.Comment: Submitted for FoSSaCS 2024. arXiv admin note: substantial text
overlap with arXiv:2304.0808
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