1,130 research outputs found
Logical operators for ontological modeling
We show that logic has more to offer to ontologists than standard first order
and modal operators. We first describe some operators of linear logic which we
believe are particularly suitable for ontological modeling, and suggest how to interpret
them within an ontological framework. After showing how they can coexist
with those of classical logic, we analyze three notions of artifact from the literature
to conclude that these linear operators allow for reducing the ontological commitment
needed for their formalization, and even simplify their logical formulation
Collection analysis for Horn clause programs
We consider approximating data structures with collections of the items that
they contain. For examples, lists, binary trees, tuples, etc, can be
approximated by sets or multisets of the items within them. Such approximations
can be used to provide partial correctness properties of logic programs. For
example, one might wish to specify than whenever the atom is proved
then the two lists and contain the same multiset of items (that is,
is a permutation of ). If sorting removes duplicates, then one would like to
infer that the sets of items underlying and are the same. Such results
could be useful to have if they can be determined statically and automatically.
We present a scheme by which such collection analysis can be structured and
automated. Central to this scheme is the use of linear logic as a omputational
logic underlying the logic of Horn clauses
Deverbal semantics and the Montagovian generative lexicon
We propose a lexical account of action nominals, in particular of deverbal
nominalisations, whose meaning is related to the event expressed by their base
verb. The literature about nominalisations often assumes that the semantics of
the base verb completely defines the structure of action nominals. We argue
that the information in the base verb is not sufficient to completely determine
the semantics of action nominals. We exhibit some data from different
languages, especially from Romance language, which show that nominalisations
focus on some aspects of the verb semantics. The selected aspects, however,
seem to be idiosyncratic and do not automatically result from the internal
structure of the verb nor from its interaction with the morphological suffix.
We therefore propose a partially lexicalist approach view of deverbal nouns. It
is made precise and computable by using the Montagovian Generative Lexicon, a
type theoretical framework introduced by Bassac, Mery and Retor\'e in this
journal in 2010. This extension of Montague semantics with a richer type system
easily incorporates lexical phenomena like the semantics of action nominals in
particular deverbals, including their polysemy and (in)felicitous
copredications.Comment: A revised version will appear in the Journal of Logic, Language and
Informatio
Unifying Functional Interpretations: Past and Future
This article surveys work done in the last six years on the unification of
various functional interpretations including G\"odel's dialectica
interpretation, its Diller-Nahm variant, Kreisel modified realizability,
Stein's family of functional interpretations, functional interpretations "with
truth", and bounded functional interpretations. Our goal in the present paper
is twofold: (1) to look back and single out the main lessons learnt so far, and
(2) to look forward and list several open questions and possible directions for
further research.Comment: 18 page
An Open Challenge Problem Repository for Systems Supporting Binders
A variety of logical frameworks support the use of higher-order abstract
syntax in representing formal systems; however, each system has its own set of
benchmarks. Even worse, general proof assistants that provide special libraries
for dealing with binders offer a very limited evaluation of such libraries, and
the examples given often do not exercise and stress-test key aspects that arise
in the presence of binders. In this paper we design an open repository ORBI
(Open challenge problem Repository for systems supporting reasoning with
BInders). We believe the field of reasoning about languages with binders has
matured, and a common set of benchmarks provides an important basis for
evaluation and qualitative comparison of different systems and libraries that
support binders, and it will help to advance the field.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759
Proofs for free - parametricity for dependent types
Reynolds' abstraction theorem shows how a typing judgement in System F can be translated into a relational statement (in second order predicate logic) about inhabitants of the type. We obtain a similar result for pure type systems: for any PTS used as a programming language, there is a PTS that can be used as a logic for parametricity. Types in the source PTS are translated to relations (expressed as types) in the target. Similarly, values of a given type are translated to proofs that the values satisfy the relational interpretation. We extend the result to inductive families. We also show that the assumption that every term satisfies the parametricity condition generated by its type is consistent with the generated logic
Model Checking Social Network Models
A social network service is a platform to build social relations among people
sharing similar interests and activities. The underlying structure of a social
networks service is the social graph, where nodes represent users and the arcs
represent the users' social links and other kind of connections. One important
concern in social networks is privacy: what others are (not) allowed to know
about us. The "logic of knowledge" (epistemic logic) is thus a good formalism
to define, and reason about, privacy policies. In this paper we consider the
problem of verifying knowledge properties over social network models (SNMs),
that is social graphs enriched with knowledge bases containing the information
that the users know. More concretely, our contributions are: i) We prove that
the model checking problem for epistemic properties over SNMs is decidable; ii)
We prove that a number of properties of knowledge that are sound w.r.t. Kripke
models are also sound w.r.t. SNMs; iii) We give a satisfaction-preserving
encoding of SNMs into canonical Kripke models, and we also characterise which
Kripke models may be translated into SNMs; iv) We show that, for SNMs, the
model checking problem is cheaper than the one based on standard Kripke models.
Finally, we have developed a proof-of-concept implementation of the
model-checking algorithm for SNMs.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
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