443 research outputs found
Fatalism and Future Contingents
In this paper I address issues related to the problem of future contingents and
the metaphysical doctrine of fatalism. Two classical responses to the problem of
future contingents are the third truth value view and the all-false view. According to
the former, future contingents take a third truth value which goes beyond truth and
falsity. According to the latter, they are all false. I here illustrate and discuss two
ways to respectively argue for those two views. Both ways are similar in spirit and
intimately connected with fatalism, in the sense that they engage with the doctrine
of fatalism and accept a large part of a standard fatalistic machinery
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear,
hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We
survey also results which show the tree different proof-theoretic frameworks
for many-valued logics, e.g. frameworks of the following deductive calculi:
Hilbert's style, sequent, and hypersequent. We present a general way that
allows to construct systematically analytic calculi for a large family of
non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and
p-adic valued logics characterized by a special format of semantics with an
appropriate rejection of Archimedes' axiom. These logics are built as different
extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's,
Product, and Post's logics). The informal sense of Archimedes' axiom is that
anything can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is infinite and it
is not well-founded and well-ordered. On the base of non-Archimedean valued
logics, we construct non-Archimedean valued interval neutrosophic logic INL by
which we can describe neutrality phenomena.Comment: 119 page
Temporal datalog with existential quantification
Existential rules, also known as tuple-generating
dependencies (TGDs) or DatalogÂą rules, are heavily studied in the communities of Knowledge
Representation and Reasoning, Semantic Web,
and Databases, due to their rich modelling capabilities. In this paper we consider TGDs in
the temporal setting, by introducing and studying DatalogMTLââan extension of metric temporal Datalog (DatalogMTL) obtained by allowing for existential rules in programs. We show that
DatalogMTLâ
is undecidable even in the restricted
cases of guarded and weakly-acyclic programs. To
address this issue we introduce uniform semantics
which, on the one hand, is well-suited for modelling temporal knowledge as it prevents from unintended value invention and, on the other hand,
provides decidability of reasoning; in particular, it
becomes 2-ExpSpace-complete for weakly-acyclic
programs but remains undecidable for guarded programs. We provide an implementation for the decidable case and demonstrate its practical feasibility. Thus we obtain an expressive, yet decidable,
rule-language and a system which is suitable for
complex temporal reasoning with existential rules
- âŚ