186 research outputs found
On Modal Logics of Partial Recursive Functions
The classical propositional logic is known to be sound and complete with
respect to the set semantics that interprets connectives as set operations. The
paper extends propositional language by a new binary modality that corresponds
to partial recursive function type constructor under the above interpretation.
The cases of deterministic and non-deterministic functions are considered and
for both of them semantically complete modal logics are described and
decidability of these logics is established
Attainable Knowledge
The article investigates an evidence-based semantics for epistemic logics in
which pieces of evidence are interpreted as equivalence relations on the
epistemic worlds. It is shown that the properties of knowledge obtained from
potentially infinitely many pieces of evidence are described by modal logic S5.
At the same time, the properties of knowledge obtained from only a finite
number of pieces of evidence are described by modal logic S4. The main
technical result is a sound and complete bi-modal logical system that describes
properties of these two modalities and their interplay
Epistemic Logic for Communication Chains
The paper considers epistemic properties of linear communication chains. It
describes a sound and complete logical system that, in addition to the standard
axioms of S5 in a multi-modal language, contains two non-trivial axioms that
capture the linear structure of communication chains.Comment: 7 pages, Contributed talk at TARK 2013 (arXiv:1310.6382)
http://www.tark.or
Marketing Impact on Diffusion in Social Networks
The paper proposes a way to add marketing into the standard threshold model
of social networks. Within this framework, the paper studies logical properties
of the influence relation between sets of agents in social networks. Two
different forms of this relation are considered: one for promotional marketing
and the other for preventive marketing. In each case a sound and complete
logical system describing properties of the influence relation is proposed.
Both systems could be viewed as extensions of Armstrong's axioms of functional
dependency from the database theory
Knowledge and Blameworthiness
Blameworthiness of an agent or a coalition of agents is often defined in
terms of the principle of alternative possibilities: for the coalition to be
responsible for an outcome, the outcome must take place and the coalition
should have had a strategy to prevent it. In this article we argue that in the
settings with imperfect information, not only should the coalition have had a
strategy, but it also should have known that it had a strategy, and it should
have known what the strategy was. The main technical result of the article is a
sound and complete bimodal logic that describes the interplay between knowledge
and blameworthiness in strategic games with imperfect information
Blameworthiness in Strategic Games
There are multiple notions of coalitional responsibility. The focus of this
paper is on the blameworthiness defined through the principle of alternative
possibilities: a coalition is blamable for a statement if the statement is
true, but the coalition had a strategy to prevent it. The main technical result
is a sound and complete bimodal logical system that describes properties of
blameworthiness in one-shot games
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