83 research outputs found
Declarative Programming with Intensional Sets in Java Using JSetL
Intensional sets are sets given by a property rather than by enumerating
their elements. In previous work, we have proposed a decision procedure for a
first-order logic language which provides Restricted Intensional Sets (RIS),
i.e., a sub-class of intensional sets that are guaranteed to denote
finite---though unbounded---sets. In this paper we show how RIS can be
exploited as a convenient programming tool also in a conventional setting,
namely, the imperative O-O language Java. We do this by considering a Java
library, called JSetL, that integrates the notions of logical variable, (set)
unification and constraints that are typical of constraint logic programming
languages into the Java language. We show how JSetL is naturally extended to
accommodate for RIS and RIS constraints, and how this extension can be
exploited, on the one hand, to support a more declarative style of programming
and, on the other hand, to effectively enhance the expressive power of the
constraint language provided by the library
Automated Reasoning with Restricted Intensional Sets
Intensional sets, i.e., sets given by a property rather than by enumerating
elements, are widely recognized as a key feature to describe complex problems
(see, e.g., specification languages such as B and Z). Notwithstanding, very few
tools exist supporting high-level automated reasoning on general formulas
involving intensional sets. In this paper we present a decision procedure for a
first-order logic language offering both extensional and (a restricted form of)
intensional sets (RIS). RIS are introduced as first-class citizens of the
language and set-theoretical operators on RIS are dealt with as constraints.
Syntactic restrictions on RIS guarantee that the denoted sets are finite,
though unbounded. The language of RIS, called L_RIS , is parametric with
respect to any first-order theory X providing at least equality and a decision
procedure for X-formulas. In particular, we consider the instance of L_RIS when
X is the theory of hereditarily finite sets and binary relations. We also
present a working implementation of this instance as part of the {log} tool and
we show through a number of examples and two case studies that, although RIS
are a subclass of general intensional sets, they are still sufficiently
expressive as to encode and solve many interesting problems. Finally, an
extensive empirical evaluation provides evidence that the tool can be used in
practice
A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases
Ontologies and rules are usually loosely coupled in knowledge representation
formalisms. In fact, ontologies use open-world reasoning while the leading
semantics for rules use non-monotonic, closed-world reasoning. One exception is
the tightly-coupled framework of Minimal Knowledge and Negation as Failure
(MKNF), which allows statements about individuals to be jointly derived via
entailment from an ontology and inferences from rules. Nonetheless, the
practical usefulness of MKNF has not always been clear, although recent work
has formalized a general resolution-based method for querying MKNF when rules
are taken to have the well-founded semantics, and the ontology is modeled by a
general oracle. That work leaves open what algorithms should be used to relate
the entailments of the ontology and the inferences of rules. In this paper we
provide such algorithms, and describe the implementation of a query-driven
system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic)
rules under the well-founded semantics and a (monotonic) ontology, represented
by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic
Programming (TPLP
On abduction and answer generation through constrained resolution
Recently, extensions of constrained logic programming and constrained resolution for theorem proving have been introduced, that consider constraints, which are interpreted under an open world assumption. We discuss relationships between applications of these approaches for query answering in knowledge base systems on the one hand and abduction-based hypothetical reasoning on the other hand. We show both that constrained resolution can be used as an operationalization of (some limited form of) abduction and that abduction is the logical status of an answer generation process through constrained resolution, ie., it is an abductive but not a deductive form of reasoning
An Automatically Verified Prototype of the Tokeneer ID Station Specification
The Tokeneer project was an initiative set forth by the National Security
Agency (NSA, USA) to be used as a demonstration that developing highly secure
systems can be made by applying rigorous methods in a cost effective manner.
Altran Praxis (UK) was selected by NSA to carry out the development of the
Tokeneer ID Station. The company wrote a Z specification later implemented in
the SPARK Ada programming language, which was verified using the SPARK Examiner
toolset. In this paper, we show that the Z specification can be easily and
naturally encoded in the {log} set constraint language, thus generating a
functional prototype. Furthermore, we show that {log}'s automated proving
capabilities can discharge all the proof obligations concerning state
invariants as well as important security properties. As a consequence, the
prototype can be regarded as correct with respect to the verified properties.
This provides empirical evidence that Z users can use {log} to generate correct
prototypes from their Z specifications. In turn, these prototypes enable or
simplify some verificatio activities discussed in the paper
A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0
We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories
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