567 research outputs found
Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer
and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We
give new analytic proof systems for A and use the embeddings to derive
corresponding systems for L. These include: hypersequent calculi for A and L
and terminating versions of these calculi; labelled single sequent calculi for
A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur
Behavioural equivalences for timed systems
Timed transition systems are behavioural models that include an explicit
treatment of time flow and are used to formalise the semantics of several
foundational process calculi and automata. Despite their relevance, a general
mathematical characterisation of timed transition systems and their behavioural
theory is still missing. We introduce the first uniform framework for timed
behavioural models that encompasses known behavioural equivalences such as
timed bisimulations, timed language equivalences as well as their weak and
time-abstract counterparts. All these notions of equivalences are naturally
organised by their discriminating power in a spectrum. We prove that this
result does not depend on the type of the systems under scrutiny: it holds for
any generalisation of timed transition system. We instantiate our framework to
timed transition systems and their quantitative extensions such as timed
probabilistic systems
De Finettian Logics of Indicative Conditionals Part II: Proof Theory and Algebraic Semantics
In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicative conditionals, most notably the proposals by de Finetti (1936) and Reichenbach (1935, 1944) on the one hand, and by Cooper ( Inquiry , 11 , 295–320, 1968) and Cantwell ( Notre Dame Journal of Formal Logic , 49 , 245–260, 2008) on the other. Here we provide the proof theory for the resulting logics and , using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: allows for algebraic completeness, but not for the construction of a canonical model, while fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects
Two-layered logics for probabilities and belief functions over Belnap--Dunn logic
This paper is an extended version of an earlier submission to WoLLIC 2023. We
discuss two-layered logics formalising reasoning with probabilities and belief
functions that combine the Lukasiewicz -valued logic with Baaz
operator and the Belnap--Dunn logic. We consider two probabilistic
logics that present two perspectives on the probabilities in the Belnap--Dunn
logic: -probabilities and -probabilities. In the first case,
every event has independent positive and negative measures that denote
the likelihoods of and , respectively. In the second case, the
measures of the events are treated as partitions of the sample into four
exhaustive and mutually exclusive parts corresponding to pure belief, pure
disbelief, conflict and uncertainty of an agent in . In addition to that,
we discuss two logics for the paraconsistent reasoning with belief and
plausibility functions. They equip events with two measures (positive and
negative) with their main difference being whether the negative measure of
is defined as the \emph{belief in } or treated independently
as \emph{the plausibility of }. We provide a sound and complete
Hilbert-style axiomatisation of the logic of -probabilities and
establish faithful translations between it and the logic of
-probabilities. We also show that the satisfiability problem in all the
logics is -complete.Comment: arXiv admin note: text overlap with arXiv:2303.0456
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