48 research outputs found
Tool support for reasoning in display calculi
We present a tool for reasoning in and about propositional sequent calculi.
One aim is to support reasoning in calculi that contain a hundred rules or
more, so that even relatively small pen and paper derivations become tedious
and error prone. As an example, we implement the display calculus D.EAK of
dynamic epistemic logic. Second, we provide embeddings of the calculus in the
theorem prover Isabelle for formalising proofs about D.EAK. As a case study we
show that the solution of the muddy children puzzle is derivable for any number
of muddy children. Third, there is a set of meta-tools, that allows us to adapt
the tool for a wide variety of user defined calculi
Distributed Transition Systems with Tags for Privacy Analysis
We present a logical framework that formally models how a given private
information P stored on a given database D, can get captured progressively, by
an agent/adversary querying the database repeatedly.Named DLTTS (Distributed
Labeled Tagged Transition System), the frame-work borrows ideas from several
domains: Probabilistic Automata of Segala, Probabilistic Concurrent Systems,
and Probabilistic labelled transition systems. To every node on a DLTTS is
attached a tag that represents the 'current' knowledge of the adversary,
acquired from the responses of the answering mechanism of the DBMS to his/her
queries, at the nodes traversed earlier, along any given run; this knowledge is
completed at the same node, with further relational deductions, possibly in
combination with 'public' information from other databases given in advance. A
'blackbox' mechanism is also part of a DLTTS, and it is meant as an oracle; its
role is to tell if the private information has been deduced by the adversary at
the current node, and if so terminate the run. An additional special feature is
that the blackbox also gives information on how 'close',or how 'far', the
knowledge of the adversary is, from the private information P , at the current
node. A metric is defined for that purpose, on the set of all 'type compatible'
tuples from the given database, the data themselves being typed with the
headers of the base. Despite the transition systems flavor of our framework,
this metric is not 'behavioral' in the sense presented in some other works. It
is exclusively database oriented,and allows to define new notions of adjacency
and of -indistinguishabilty between databases, more generally than those
usually based on the Hamming metric (and a restricted notion of adjacency).
Examples are given all along to illustrate how our framework works.
Keywords:Database, Privacy, Transition System, Probability, Distribution
Fuzzy bi-G\"{o}del modal logic and its paraconsistent relatives
We present the axiomatisation of the fuzzy bi-G\"{o}del modal logic
(formulated in the language containing and treating the
coimplication as a defined connective) and establish its PSpace-completeness.
We also consider its paraconsistent relatives defined on fuzzy frames with two
valuations and standing for the support of truth and falsity,
respectively, and equipped with \emph{two fuzzy relations} and used
to determine supports of truth and falsity of modal formulas. We establish
embeddings of these paraconsistent logics into the fuzzy bi-G\"{o}del modal
logic and use them to prove their PSpace-completeness and obtain the
characterisation of definable frames
Constraint tableaux for two-dimensional fuzzy logics
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del
logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted
on matrices, where the common underlying structure is the bi-lattice (twisted)
product of the interval. The first (resp.\ second) coordinate encodes
the positive (resp.\ negative) information one has about a statement. We
propose constraint tableaux that provide a modular framework to address their
completeness and complexity
Presumptive Reasoning in a Paraconsistent Setting
We explore presumptive reasoning in the paraconsistent case. Specifically, we
provide semantics for non-trivial reasoning with presumptive arguments with
contradictory assumptions or conclusions. We adapt the case models proposed by
Verheij and define the paraconsistent analogues of the three types of validity
defined therein: coherent, presumptively valid, and conclusive ones. To
formalise the reasoning, we define case models that use ,
an expansion of the Belnap--Dunn logic with the Baaz Delta operator. We also
show how to recover presumptive reasoning in the original, classical context
from our paraconsistent version of case models. Finally, we construct
a~two-layered logic over and (an
expansion of G\"{o}del logic with a coimplication or ) and obtain a
faithful translation of presumptive arguments into formulas