114 research outputs found
Axiomatizing the lexicographic products of modal logics with linear temporal logic
Given modal logics L1 and L2, their lexicographic product L1 x L2 is a new logic whose frames are the Cartesian products of an L1-frame and an L2-frame, but with the new accessibility relations reminiscent of a lexicographic ordering. This article considers the lexicographic products of several modal logics with linear temporal logic (LTL) based on ``next'' and ``always in the future''. We provide axiomatizations for logics of the form L x LTL and define cover-simple classes of frames; we then prove that, under fairly general conditions, our axiomatizations are sound and complete whenever the class of L-frames is cover-simple. Finally, we prove completeness for several concrete logics of the form L x LTL
Decidability and complexity via mosaics of the temporal logic of the lexicographic products of unbounded dense linear orders
This article considers the temporal logic of the lexicographic products of unbounded dense linear orders and provides via mosaics a complete decision procedure in nondeterministic polynomial time for the satisfiability problem it gives rise to
Sufficient conditions for local tabularity of a polymodal logic
On relational structures and on polymodal logics, we describe operations
which preserve local tabularity. This provides new sufficient semantic and
axiomatic conditions for local tabularity of a modal logic. The main results
are the following.
We show that local tabularity does not depend on reflexivity. Namely, given a
class of frames, consider the class of
frames, where the reflexive closure operation was applied to each relation in
every frame in . We show that if the logic of
is locally tabular, then the logic of is
locally tabular as well.
Then we consider the operation of sum on Kripke frames, where a family of
frames-summands is indexed by elements of another frame. We show that if both
the logic of indices and the logic of summands are locally tabular, then the
logic of corresponding sums is also locally tabular.
Finally, using the previous theorem, we describe an operation on logics that
preserves local tabularity: we provide a set of formulas such that the
extension of the fusion of two canonical locally tabular logics with these
formulas is locally tabular
Team logic : axioms, expressiveness, complexity
Team semantics is an extension of classical logic where statements do not refer to single states of a system, but instead to sets of such states, called teams. This kind of semantics has applications for example in mathematical logic, verification of dynamic systems as well as in database theory.
In this thesis, we focus on the propositional, modal and first-order variant of team logic.
We study the classical questions of formal logic: Expressiveness (can we formalize sufficiently interesting properties of models?), axiomatizability (can all true statements be deduced in some formal system?) and complexity (can problems such as satisfiability and model checking be solved algorithmically?). Finally, we classify existing team logics and show approaches how team semantics can be defined for arbitrary other logics.Team-Semantik ist eine Erweiterung klassischer Logik, bei der Aussagen nicht über einzelne Zustände eines Systems getroffen werden, sondern über Mengen solcher Zustände, genannt Teams. Diese Art von Semantik besitzt unter anderem Anwendungen in der mathematischen Logik, in der Verifikation dynamischer Systeme sowie in der Datenbanktheorie. In dieser Arbeit liegt der Fokus auf der aussagenlogischen, der modallogischen und der prädikatenlogischen Variante der Team-Logik. Es werden die klassischen Fragestellungen formaler Logik untersucht: Ausdruckskraft (können hinreichend interessante Eigenschaften von Modellen formalisiert werden?), Axiomatisierbarkeit (lassen sich alle wahren Aussagen in einem Kalkül ableiten?) und Komplexität (können Probleme wie Erfüllbarkeit und Modellprüfung algorithmisch gelöst werden?). Schlussendlich werden existierende Team-Logiken klassifiziert und es werden Ansätze aufgezeigt, wie Team-Semantik für beliebige weitere Logiken definiert werden kann
Probabilistic logics based on Riesz spaces
We introduce a novel real-valued endogenous logic for expressing properties
of probabilistic transition systems called Riesz modal logic. The design of the
syntax and semantics of this logic is directly inspired by the theory of Riesz
spaces, a mature field of mathematics at the intersection of universal algebra
and functional analysis. By using powerful results from this theory, we develop
the duality theory of the Riesz modal logic in the form of an
algebra-to-coalgebra correspondence. This has a number of consequences
including: a sound and complete axiomatization, the proof that the logic
characterizes probabilistic bisimulation and other convenient results such as
completion theorems. This work is intended to be the basis for subsequent
research on extensions of Riesz modal logic with fixed-point operators
Coalition logic with individual, distributed and common knowledge
Coalition logic is currently one of the most popular logics for multi-agent systems. While logics combining coalitional and epistemic operators have received considerable attention, completeness results for epistemic extensions of coalition logic have so far been missing. In this paper we provide several such results and proofs.We prove completeness for epistemic coalition logic with common knowledge, with distributed knowledge, and with both common and distributed knowledge, respectively. Furthermore, we completely characterise the complexity of the satisfiability problem for each of the three logics. We also study logics with interaction axioms connecting coalitional ability and knowledge
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