10,671 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
Ceteris paribus conditionals and comparative normalcy
Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals â that is, conditionals that incorporate a ceteris paribus or âother things being equalâ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species of variably strict conditional I hope to shed new light upon their content and their logic
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Knowing Values and Public Inspection
We present a basic dynamic epistemic logic of "knowing the value". Analogous
to public announcement in standard DEL, we study "public inspection", a new
dynamic operator which updates the agents' knowledge about the values of
constants. We provide a sound and strongly complete axiomatization for the
single and multi-agent case, making use of the well-known Armstrong axioms for
dependencies in databases
The Broadest Necessity
In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given
- âŠ