781 research outputs found
Logic of Non-Monotonic Interactive Proofs (Formal Theory of Temporary Knowledge Transfer)
We propose a monotonic logic of internalised non-monotonic or instant
interactive proofs (LiiP) and reconstruct an existing monotonic logic of
internalised monotonic or persistent interactive proofs (LiP) as a minimal
conservative extension of LiiP. Instant interactive proofs effect a fragile
epistemic impact in their intended communities of peer reviewers that consists
in the impermanent induction of the knowledge of their proof goal by means of
the knowledge of the proof with the interpreting reviewer: If my peer reviewer
knew my proof then she would at least then (in that instant) know that its
proof goal is true. Their impact is fragile and their induction of knowledge
impermanent in the sense of being the case possibly only at the instant of
learning the proof. This accounts for the important possibility of
internalising proofs of statements whose truth value can vary, which, as
opposed to invariant statements, cannot have persistent proofs. So instant
interactive proofs effect a temporary transfer of certain propositional
knowledge (knowable ephemeral facts) via the transmission of certain individual
knowledge (knowable non-monotonic proofs) in distributed systems of multiple
interacting agents.Comment: continuation of arXiv:1201.3667 ; published extended abstract:
DOI:10.1007/978-3-642-36039-8_16 ; related to arXiv:1208.591
Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)
We produce a decidable classical normal modal logic of internalised
negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP)
from an existing logical counterpart of non-monotonic or instant interactive
proofs (LiiP). LDiiP internalises agent-centric proof theories that are
negation-complete (maximal) and consistent (and hence strictly weaker than, for
example, Peano Arithmetic) and enjoy the disjunction property (like
Intuitionistic Logic). In other words, internalised proof theories are
ultrafilters and all internalised proof goals are definite in the sense of
being either provable or disprovable to an agent by means of disjunctive
internalised proofs (thus also called epistemic deciders). Still, LDiiP itself
is classical (monotonic, non-constructive), negation-incomplete, and does not
have the disjunction property. The price to pay for the negation completeness
of our interactive proofs is their non-monotonicity and non-communality (for
singleton agent communities only). As a normal modal logic, LDiiP enjoys a
standard Kripke-semantics, which we justify by invoking the Axiom of Choice on
LiiP's and then construct in terms of a concrete oracle-computable function.
LDiiP's agent-centric internalised notion of proof can also be viewed as a
negation-complete disjunctive explicit refinement of standard KD45-belief, and
yields a disjunctive but negation-incomplete explicit refinement of
S4-provability.Comment: Expanded Introduction. Added Footnote 4. Corrected Corollary 3 and 4.
Continuation of arXiv:1208.184
Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)
We produce a decidable super-intuitionistic normal modal logic of
internalised intuitionistic (and thus disjunctive and monotonic) interactive
proofs (LIiP) from an existing classical counterpart of classical monotonic
non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs
effect a durable epistemic impact in the possibly adversarial communication
medium CM (which is imagined as a distinguished agent), and only in that, that
consists in the permanent induction of the perfect and thus disjunctive
knowledge of their proof goal by means of CM's knowledge of the proof: If CM
knew my proof then CM would persistently and also disjunctively know that my
proof goal is true. So intuitionistic interactive proofs effect a lasting
transfer of disjunctive propositional knowledge (disjunctively knowable facts)
in the communication medium of multi-agent distributed systems via the
transmission of certain individual knowledge (knowable intuitionistic proofs).
Our (necessarily) CM-centred notion of proof is also a disjunctive explicit
refinement of KD45-belief, and yields also such a refinement of standard
S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP,
and their internalised notions of proof. As a side-effect, we offer a short
internalised proof of the Disjunction Property of Intuitionistic Logic
(originally proved by Goedel).Comment: continuation of arXiv:1201.3667; extended start of Section 1 and 2.1;
extended paragraph after Fact 1; dropped the N-rule as primitive and proved
it derivable; other, non-intuitionistic family members: arXiv:1208.1842,
arXiv:1208.591
Parametric Constructive Kripke-Semantics for Standard Multi-Agent Belief and Knowledge (Knowledge As Unbiased Belief)
We propose parametric constructive Kripke-semantics for multi-agent
KD45-belief and S5-knowledge in terms of elementary set-theoretic constructions
of two basic functional building blocks, namely bias (or viewpoint) and
visibility, functioning also as the parameters of the doxastic and epistemic
accessibility relation. The doxastic accessibility relates two possible worlds
whenever the application of the composition of bias with visibility to the
first world is equal to the application of visibility to the second world. The
epistemic accessibility is the transitive closure of the union of our doxastic
accessibility and its converse. Therefrom, accessibility relations for common
and distributed belief and knowledge can be constructed in a standard way. As a
result, we obtain a general definition of knowledge in terms of belief that
enables us to view S5-knowledge as accurate (unbiased and thus true)
KD45-belief, negation-complete belief and knowledge as exact KD45-belief and
S5-knowledge, respectively, and perfect S5-knowledge as precise (exact and
accurate) KD45-belief, and all this generically for arbitrary functions of bias
and visibility. Our results can be seen as a semantic complement to previous
foundational results by Halpern et al. about the (un)definability and
(non-)reducibility of knowledge in terms of and to belief, respectively
Deductive verification of object-oriented software : dynamic frames, dynamic logic and predicate abstraction
Software systems play a central role in modern society, and their correctness is often crucially important. Formal specification and verification are promising approaches for ensuring correctness more rigorously than just by testing. This work presents an approach for deductively verifying design-by-contract specifications of object-oriented programs. The approach is based on dynamic logic, and addresses the challenges of modularity and automation using dynamic frames and predicate abstraction
Incremental and Modular Context-sensitive Analysis
Context-sensitive global analysis of large code bases can be expensive, which
can make its use impractical during software development. However, there are
many situations in which modifications are small and isolated within a few
components, and it is desirable to reuse as much as possible previous analysis
results. This has been achieved to date through incremental global analysis
fixpoint algorithms that achieve cost reductions at fine levels of granularity,
such as changes in program lines. However, these fine-grained techniques are
not directly applicable to modular programs, nor are they designed to take
advantage of modular structures. This paper describes, implements, and
evaluates an algorithm that performs efficient context-sensitive analysis
incrementally on modular partitions of programs. The experimental results show
that the proposed modular algorithm shows significant improvements, in both
time and memory consumption, when compared to existing non-modular, fine-grain
incremental analysis techniques. Furthermore, thanks to the proposed
inter-modular propagation of analysis information, our algorithm also
outperforms traditional modular analysis even when analyzing from scratch.Comment: 56 pages, 27 figures. To be published in Theory and Practice of Logic
Programming. v3 corresponds to the extended version of the ICLP2018 Technical
Communication. v4 is the revised version submitted to Theory and Practice of
Logic Programming. v5 (this one) is the final author version to be published
in TPL
Mechanising an algebraic rely-guarantee refinement calculus
PhD ThesisDespite rely-guarantee (RG) being a well-studied program logic established in the 1980s, it
was not until recently that researchers realised that rely and guarantee conditions could be
treated as independent programming constructs. This recent reformulation of RG paved the
way to algebraic characterisations which have helped to better understand the difficulties that
arise in the practical application of this development approach.
The primary focus of this thesis is to provide automated tool support for a rely-guarantee
refinement calculus proposed by Hayes et. al., where rely and guarantee are defined as
independent commands. Our motivation is to investigate the application of an algebraic
approach to derive concrete examples using this calculus. In the course of this thesis, we
locate and fix a few issues involving the refinement language, its operational semantics and
preexisting proofs. Moreover, we extend the refinement calculus of Hayes et. al. to cover
indexed parallel composition, non-atomic evaluation of expressions within specifications,
and assignment to indexed arrays. These extensions are illustrated via concrete examples.
Special attention is given to design decisions that simplify the application of the mechanised
theory. For example, we leave part of the design of the expression language on the
hands of the user, at the cost of the requiring the user to define the notion of undefinedness
for unary and binary operators; and we also formalise a notion of indexed parallelism that is
parametric on the type of the indexes, this is done deliberately to simplify the formalisation of
algorithms. Additionally, we use stratification to reduce the number of cases in in simulation
proofs involving the operational semantics. Finally, we also use the algebra to discuss the
role of types in program derivation
Dagstuhl News January - December 2001
"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic
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