595 research outputs found
Complexity Results for Modal Dependence Logic
Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances
the basic modal language by an operator =(). For propositional variables
p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is
determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation,
2009) showed that satisfiability for modal dependence logic is complete for
nondeterministic exponential time. In this paper we consider fragments of modal
dependence logic obtained by restricting the set of allowed propositional
connectives. We show that satisfibility for poor man's dependence logic, the
language consisting of formulas built from literals and dependence atoms using
conjunction, necessity and possibility (i.e., disallowing disjunction), remains
NEXPTIME-complete. If we only allow monotone formulas (without negation, but
with disjunction), the complexity drops to PSPACE-completeness. We also extend
V\"a\"an\"anen's language by allowing classical disjunction besides dependence
disjunction and show that the satisfiability problem remains NEXPTIME-complete.
If we then disallow both negation and dependence disjunction, satistiability is
complete for the second level of the polynomial hierarchy. In this way we
completely classify the computational complexity of the satisfiability problem
for all restrictions of propositional and dependence operators considered by
V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape
Impossible worlds
Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well as possible worlds. So what are impossible worlds? Graham Priest claims that any of the usual stories about possible worlds can be told about impossible worlds, too. But far from it. I'll argue that impossible worlds cannot be genuine worlds, of the kind proposed by Lewis, McDaniel or Yagisawa. Nor can they be ersatz worlds on the model proposed by Melia or Sider. Constructing impossible worlds, it turns out, requires novel metaphysical resources
Safety, the Preface Paradox and Possible Worlds Semantics
This paper contains an argument to the effect that possible worlds semantics renders
semantic knowledge impossible, no matter what ontological interpretation is given
to possible worlds. The essential contention made is that possible worlds semantic
knowledge is unsafe and this is shown by a parallel with the preface paradox
Community of inquiry and inquiry-based learning
Peer reviewe
Rich Situated Attitudes
We outline a novel theory of natural language meaning, Rich
Situated Semantics [RSS], on which the content of sentential utterances
is semantically rich and informationally situated. In virtue of its situatedness,
an utterance’s rich situated content varies with the informational
situation of the cognitive agent interpreting the utterance. In virtue of its
richness, this content contains information beyond the utterance’s lexically
encoded information. The agent-dependence of rich situated content
solves a number of problems in semantics and the philosophy of language
(cf. [14, 20, 25]). In particular, since RSS varies the granularity of utterance
contents with the interpreting agent’s informational situation, it
solves the problem of finding suitably fine- or coarse-grained objects for
the content of propositional attitudes. In virtue of this variation, a layman
will reason with more propositions than an expert
Game theoretical semantics for some non-classical logics
Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values
Probabilistic Consensus of the Blockchain Protocol
We introduce a temporal epistemic logic with probabilities as an extension of temporal epistemic logic. This extension enables us to reason about properties that characterize the uncertain nature of knowledge, like “agent a will with high probability know after time s same fact”. To define semantics for the logic we enrich temporal epistemic Kripke models with probability functions defined on sets of possible worlds. We use this framework to model and reason about probabilistic properties of the blockchain protocol, which is in essence probabilistic since ledgers are immutable with high probabilities. We prove the probabilistic convergence for reaching the consensus of the protocol
Theory of Concepts
UID/FIL/00183/2013authorsversionpublishe
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