33 research outputs found
Uncertainty About Evidence
We develop a logical framework for reasoning about knowledge and evidence in
which the agent may be uncertain about how to interpret their evidence. Rather
than representing an evidential state as a fixed subset of the state space, our
models allow the set of possible worlds that a piece of evidence corresponds to
to vary from one possible world to another, and therefore itself be the subject
of uncertainty. Such structures can be viewed as (epistemically motivated)
generalizations of topological spaces. In this context, there arises a natural
distinction between what is actually entailed by the evidence and what the
agent knows is entailed by the evidence -- with the latter, in general, being
much weaker. We provide a sound and complete axiomatization of the
corresponding bi-modal logic of knowledge and evidence entailment, and
investigate some natural extensions of this core system, including the addition
of a belief modality and its interaction with evidence interpretation and
entailment, and the addition of a "knowability" modality interpreted via a
(generalized) interior operator.Comment: In Proceedings TARK 2019, arXiv:1907.0833
Symbolic Analysis of Maude Theories with Narval
[EN] Concurrent functional languages that are endowed with symbolic reasoning capabilities such as Maude offer a high-level, elegant, and efficient approach to programming and analyzing complex, highly nondeterministic software systems. Maude's symbolic capabilities are based on equational unification and narrowing in rewrite theories, and provide Maude with advanced logic programming capabilities such as unification modulo user-definable equational theories and symbolic reachability analysis in rewrite theories. Intricate computing problems may be effectively and naturally solved in Maude thanks to the synergy of these recently developed symbolic capabilities and classical Maude features, such as: (i) rich type structures with sorts (types), subsorts, and overloading; (ii) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity; and (iii) classical reachability analysis in rewrite theories. However, the combination of all of these features may hinder the understanding of Maude symbolic computations for non-experienced developers. The purpose of this article is to describe how programming and analysis of Maude rewrite theories can be made easier by providing a sophisticated graphical tool called Narval that supports the fine-grained inspection of Maude symbolic computations.This work has been partially supported by the EU (FEDER) and the Spanish MCIU under grant RTI2018-094403-B-C32, by the Spanish Generalitat Valenciana under grants PROMETEO/2019/098 and APOSTD/2019/127, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286.Alpuente Frasnedo, M.; Escobar Román, S.; Sapiña-Sanchis, J.; Ballis, D. (2019). Symbolic Analysis of Maude Theories with Narval. Theory and Practice of Logic Programming. 19(5-6):874-890. https://doi.org/10.1017/S1471068419000243S874890195-
Logic of Justified Beliefs Based on Argumentation
This manuscript presents a topological argumentation framework for modelling notions of evidence-based (i.e., justified) belief. Our framework relies on so-called topological evidence models to represent the pieces of evidence that an agent has at her disposal, and it uses abstract argumentation theory to select the pieces of evidence that the agent will use to define her beliefs. The tools from abstract argumentation theory allow us to model agents who make decisions in the presence of contradictory information. Thanks to this, it is possible to define two new notions of beliefs, grounded beliefs and fully grounded beliefs. These notions are discussed in this paper, analysed and compared with the existing notion of topological justified belief. This comparison revolves around three main issues: closure under conjunction introduction, the level of consistency and their logical strength.acceptedVersio
Expressivity Within Second-Order Transitive-Closure Logic
Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in a natural and elegant manner. As SO(TC) offers an attractive framework for expressing properties in terms of declaratively specified computations, it is interesting to understand the expressivity of different features of the language. This paper focuses on the fragment MSO(TC), as well on the purely existential fragment SO(2TC)(exists); in 2TC, the TC operator binds only tuples of relation variables. We establish that, with respect to expressive power, SO(2TC)(exists) collapses to existential first-order logic. In addition we study the relationship of MSO(TC) to an extension of MSO(TC) with counting features (CMSO(TC)) as well as to order-invariant MSO. We show that the expressive powers of CMSO(TC) and MSO(TC) coincide. Moreover we establish that, over unary vocabularies, MSO(TC) strictly subsumes order-invariant MSO
Variant-based Equational Unification under Constructor Symbols
Equational unification of two terms consists of finding a substitution that,
when applied to both terms, makes them equal modulo some equational properties.
A narrowing-based equational unification algorithm relying on the concept of
the variants of a term is available in the most recent version of Maude,
version 3.0, which provides quite sophisticated unification features. A variant
of a term t is a pair consisting of a substitution sigma and the canonical form
of tsigma. Variant-based unification is decidable when the equational theory
satisfies the finite variant property. However, this unification procedure does
not take into account constructor symbols and, thus, may compute many more
unifiers than the necessary or may not be able to stop immediately. In this
paper, we integrate the notion of constructor symbol into the variant-based
unification algorithm. Our experiments on positive and negative unification
problems show an impressive speedup.Comment: In Proceedings ICLP 2020, arXiv:2009.09158. arXiv admin note:
substantial text overlap with arXiv:1909.0824
Quantum Information Effects
We study the two dual quantum information effects to manipulate the amount of
information in quantum computation: hiding and allocation. The resulting
type-and-effect system is fully expressive for irreversible quantum computing,
including measurement. We provide universal categorical constructions that
semantically interpret this arrow metalanguage with choice, starting with any
rig groupoid interpreting the reversible base language. Several properties of
quantum measurement follow in general, and we translate quantum flow charts
into our language. The semantic constructions turn the category of unitaries
between Hilbert spaces into the category of completely positive
trace-preserving maps, and they turn the category of bijections between finite
sets into the category of functions with chosen garbage. Thus they capture the
fundamental theorems of classical and quantum reversible computing of Toffoli
and Stinespring.Comment: 32 pages, including 10 page appendi