3,562 research outputs found
Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate
On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi
Qualitative calculi play a central role in representing and reasoning about
qualitative spatial and temporal knowledge. This paper studies distributive
subalgebras of qualitative calculi, which are subalgebras in which (weak)
composition distributives over nonempty intersections. It has been proven for
RCC5 and RCC8 that path consistent constraint network over a distributive
subalgebra is always minimal and globally consistent (in the sense of strong
-consistency) in a qualitative sense. The well-known subclass of convex
interval relations provides one such an example of distributive subalgebras.
This paper first gives a characterisation of distributive subalgebras, which
states that the intersection of a set of relations in the subalgebra
is nonempty if and only if the intersection of every two of these relations is
nonempty. We further compute and generate all maximal distributive subalgebras
for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra,
and Rectangle Algebra. Lastly, we establish two nice properties which will play
an important role in efficient reasoning with constraint networks involving a
large number of variables.Comment: Adding proof of Theorem 2 to appendi
Algebraic Properties of Qualitative Spatio-Temporal Calculi
Qualitative spatial and temporal reasoning is based on so-called qualitative
calculi. Algebraic properties of these calculi have several implications on
reasoning algorithms. But what exactly is a qualitative calculus? And to which
extent do the qualitative calculi proposed meet these demands? The literature
provides various answers to the first question but only few facts about the
second. In this paper we identify the minimal requirements to binary
spatio-temporal calculi and we discuss the relevance of the according axioms
for representation and reasoning. We also analyze existing qualitative calculi
and provide a classification involving different notions of a relation algebra.Comment: COSIT 2013 paper including supplementary materia
A Focused Sequent Calculus Framework for Proof Search in Pure Type Systems
Basic proof-search tactics in logic and type theory can be seen as the
root-first applications of rules in an appropriate sequent calculus, preferably
without the redundancies generated by permutation of rules. This paper
addresses the issues of defining such sequent calculi for Pure Type Systems
(PTS, which were originally presented in natural deduction style) and then
organizing their rules for effective proof-search. We introduce the idea of
Pure Type Sequent Calculus with meta-variables (PTSCalpha), by enriching the
syntax of a permutation-free sequent calculus for propositional logic due to
Herbelin, which is strongly related to natural deduction and already well
adapted to proof-search. The operational semantics is adapted from Herbelin's
and is defined by a system of local rewrite rules as in cut-elimination, using
explicit substitutions. We prove confluence for this system. Restricting our
attention to PTSC, a type system for the ground terms of this system, we obtain
the Subject Reduction property and show that each PTSC is logically equivalent
to its corresponding PTS, and the former is strongly normalising iff the latter
is. We show how to make the logical rules of PTSC into a syntax-directed system
PS for proof-search, by incorporating the conversion rules as in
syntax-directed presentations of the PTS rules for type-checking. Finally, we
consider how to use the explicitly scoped meta-variables of PTSCalpha to
represent partial proof-terms, and use them to analyse interactive proof
construction. This sets up a framework PE in which we are able to study
proof-search strategies, type inhabitant enumeration and (higher-order)
unification
Node coarsening calculi for program slicing
Several approaches to reverse and re-engineering are based upon program slicing. Unfortunately, for large systems, such as those which typically form the subject of reverse engineering activities, the space and time requirements of slicing can be a barrier to successful application. Faced with this problem, several authors have found it helpful to merge control flow graph (CFG) nodes, thereby improving the space and time requirements of standard slicing algorithms. The node-merging process essentially creates a 'coarser' version of the original CFG. The paper introduces a theory for defining control flow graph node coarsening calculi. The theory formalizes properties of interest, when coarsening is used as a precursor to program slicing. The theory is illustrated with a case study of a coarsening calculus, which is proved to have the desired properties of sharpness and consistency
QPCF: higher order languages and quantum circuits
qPCF is a paradigmatic quantum programming language that ex- tends PCF with
quantum circuits and a quantum co-processor. Quantum circuits are treated as
classical data that can be duplicated and manipulated in flexible ways by means
of a dependent type system. The co-processor is essentially a standard QRAM
device, albeit we avoid to store permanently quantum states in between two
co-processor's calls. Despite its quantum features, qPCF retains the classic
programming approach of PCF. We introduce qPCF syntax, typing rules, and its
operational semantics. We prove fundamental properties of the system, such as
Preservation and Progress Theorems. Moreover, we provide some higher-order
examples of circuit encoding
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