2,545 research outputs found
Efficient First-Order Temporal Logic for Infinite-State Systems
In this paper we consider the specification and verification of
infinite-state systems using temporal logic. In particular, we describe
parameterised systems using a new variety of first-order temporal logic that is
both powerful enough for this form of specification and tractable enough for
practical deductive verification. Importantly, the power of the temporal
language allows us to describe (and verify) asynchronous systems, communication
delays and more complex properties such as liveness and fairness properties.
These aspects appear difficult for many other approaches to infinite-state
verification.Comment: 16 pages, 2 figure
A System for Deduction-based Formal Verification of Workflow-oriented Software Models
The work concerns formal verification of workflow-oriented software models
using deductive approach. The formal correctness of a model's behaviour is
considered. Manually building logical specifications, which are considered as a
set of temporal logic formulas, seems to be the significant obstacle for an
inexperienced user when applying the deductive approach. A system, and its
architecture, for the deduction-based verification of workflow-oriented models
is proposed. The process of inference is based on the semantic tableaux method
which has some advantages when compared to traditional deduction strategies.
The algorithm for an automatic generation of logical specifications is
proposed. The generation procedure is based on the predefined workflow patterns
for BPMN, which is a standard and dominant notation for the modeling of
business processes. The main idea for the approach is to consider patterns,
defined in terms of temporal logic,as a kind of (logical) primitives which
enable the transformation of models to temporal logic formulas constituting a
logical specification. Automation of the generation process is crucial for
bridging the gap between intuitiveness of the deductive reasoning and the
difficulty of its practical application in the case when logical specifications
are built manually. This approach has gone some way towards supporting,
hopefully enhancing our understanding of, the deduction-based formal
verification of workflow-oriented models.Comment: International Journal of Applied Mathematics and Computer Scienc
Deciding regular grammar logics with converse through first-order logic
We provide a simple translation of the satisfiability problem for regular
grammar logics with converse into GF2, which is the intersection of the guarded
fragment and the 2-variable fragment of first-order logic. This translation is
theoretically interesting because it translates modal logics with certain frame
conditions into first-order logic, without explicitly expressing the frame
conditions.
A consequence of the translation is that the general satisfiability problem
for regular grammar logics with converse is in EXPTIME. This extends a previous
result of the first author for grammar logics without converse. Using the same
method, we show how some other modal logics can be naturally translated into
GF2, including nominal tense logics and intuitionistic logic.
In our view, the results in this paper show that the natural first-order
fragment corresponding to regular grammar logics is simply GF2 without extra
machinery such as fixed point-operators.Comment: 34 page
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL)
and duration calculus (DC) with infinite intervals and complete Hilbert-style
proof systems for them. The completeness results are a strong completeness
theorem for the system of probabilistic ITL with respect to an abstract
semantics and a relative completeness theorem for the system of probabilistic
DC with respect to real-time semantics. The proposed systems subsume
probabilistic real-time DC as known from the literature. A correspondence
between the proposed systems and a system of probabilistic interval temporal
logic with finite intervals and expanding modalities is established too.Comment: 43 page
An Objection to Naturalism and Atheism from Logic
I proffer a success argument for classical logical consequence. I articulate in what sense that notion of consequence should be regarded as the privileged notion for metaphysical inquiry aimed at uncovering the fundamental nature of the world. Classical logic breeds necessitism. I use necessitism to produce problems for both ontological naturalism and atheism
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