5,630 research outputs found
Cyclic proof systems for modal fixpoint logics
This thesis is about cyclic and ill-founded proof systems for modal fixpoint logics, with and without explicit fixpoint quantifiers.Cyclic and ill-founded proof-theory allow proofs with infinite branches or paths, as long as they satisfy some correctness conditions ensuring the validity of the conclusion. In this dissertation we design a few cyclic and ill-founded systems: a cyclic one for the weak Grzegorczyk modal logic K4Grz, based on our explanation of the phenomenon of cyclic companionship; and ill-founded and cyclic ones for the full computation tree logic CTL* and the intuitionistic linear-time temporal logic iLTL. All systems are cut-free, and the cyclic ones for K4Grz and iLTL have fully finitary correctness conditions.Lastly, we use a cyclic system for the modal mu-calculus to obtain a proof of the uniform interpolation property for the logic which differs from the original, automata-based one
Probabilistic Programming Interfaces for Random Graphs::Markov Categories, Graphons, and Nominal Sets
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programming language corresponds to a graphon, and conversely, every graphon arises in this way.We provide three constructions for showing that every graphon arises from an equational theory. The first is an abstract construction, using Markov categories and monoidal indeterminates. The second and third are more concrete. The second is in terms of traditional measure theoretic probability, which covers 'black-and-white' graphons. The third is in terms of probability monads on the nominal sets of Gabbay and Pitts. Specifically, we use a variation of nominal sets induced by the theory of graphs, which covers Erdős-Rényi graphons. In this way, we build new models of graph probabilistic programming from graphons
Fragments and frame classes:Towards a uniform proof theory for modal fixed point logics
This thesis studies the proof theory of modal fixed point logics. In particular, we construct proof systems for various fragments of the modal mu-calculus, interpreted over various classes of frames. With an emphasis on uniform constructions and general results, we aim to bring the relatively underdeveloped proof theory of modal fixed point logics closer to the well-established proof theory of basic modal logic. We employ two main approaches. First, we seek to generalise existing methods for basic modal logic to accommodate fragments of the modal mu-calculus. We use this approach for obtaining Hilbert-style proof systems. Secondly, we adapt existing proof systems for the modal mu-calculus to various classes of frames. This approach yields proof systems which are non-well-founded, or cyclic.The thesis starts with an introduction and some mathematical preliminaries. In Chapter 3 we give hypersequent calculi for modal logic with the master modality, building on work by Ori Lahav. This is followed by an Intermezzo, where we present an abstract framework for cyclic proofs, in which we give sufficient conditions for establishing the bounded proof property. In Chapter 4 we generalise existing work on Hilbert-style proof systems for PDL to the level of the continuous modal mu-calculus. Chapter 5 contains a novel cyclic proof system for the alternation-free two-way modal mu-calculus. Finally, in Chapter 6, we present a cyclic proof system for Guarded Kleene Algebra with Tests and take a first step towards using it to establish the completeness of an algebraic counterpart
The Infimum Problem as a Generalization of the Inclusion Problem for Automata
This thesis is concerned with automata over infinite trees. They are given a labeled infinite tree and accept or reject this tree based on its labels. A generalization of these automata with binary decisions are weighted automata. They do not just decide 'yes' or 'no', but rather compute an arbitrary value from a given algebraic structure, e.g., a semiring or a lattice. When passing from unweighted to weighted formalisms, many problems can be translated accordingly. The purpose of this work is to determine the feasibility of solving the inclusion problem for automata on infinite trees and its generalization to weighted automata, the infimum aggregation problem
Computational and experimental studies on the reaction mechanism of bio-oil components with additives for increased stability and fuel quality
As one of the world’s largest palm oil producers, Malaysia encountered a major disposal problem as vast amount of oil palm biomass wastes are produced. To overcome this problem, these biomass wastes can be liquefied into biofuel with fast pyrolysis technology. However, further upgradation of fast pyrolysis bio-oil via direct solvent addition was required to overcome it’s undesirable attributes. In addition, the high production cost of biofuels often hinders its commercialisation. Thus, the designed solvent-oil blend needs to achieve both fuel functionality and economic targets to be competitive with the conventional diesel fuel.
In this thesis, a multi-stage computer-aided molecular design (CAMD) framework was employed for bio-oil solvent design. In the design problem, molecular signature descriptors were applied to accommodate different classes of property prediction models. However, the complexity of the CAMD problem increases as the height of signature increases due to the combinatorial nature of higher order signature. Thus, a consistency rule was developed reduce the size of the CAMD problem. The CAMD problem was then further extended to address the economic aspects via fuzzy multi-objective optimisation approach.
Next, a rough-set based machine learning (RSML) model has been proposed to correlate the feedstock characterisation and pyrolysis condition with the pyrolysis bio-oil properties by generating decision rules. The generated decision rules were analysed from a scientific standpoint to identify the underlying patterns, while ensuring the rules were logical. The decision rules generated can be used to select optimal feedstock composition and pyrolysis condition to produce pyrolysis bio-oil of targeted fuel properties.
Next, the results obtained from the computational approaches were verified through experimental study. The generated pyrolysis bio-oils were blended with the identified solvents at various mixing ratio. In addition, emulsification of the solvent-oil blend in diesel was also conducted with the help of surfactants. Lastly, potential extensions and prospective work for this study have been discuss in the later part of this thesis. To conclude, this thesis presented the combination of computational and experimental approaches in upgrading the fuel properties of pyrolysis bio-oil. As a result, high quality biofuel can be generated as a cleaner burning replacement for conventional diesel fuel
Language integrated relational lenses
Relational databases are ubiquitous. Such monolithic databases accumulate large
amounts of data, yet applications typically only work on small portions of the data
at a time. A subset of the database defined as a computation on the underlying
tables is called a view. Querying views is helpful, but it is also desirable to update
them and have these changes be applied to the underlying database. This view
update problem has been the subject of much previous work before, but support
by database servers is limited and only rarely available.
Lenses are a popular approach to bidirectional transformations, a generalization
of the view update problem in databases to arbitrary data. However, perhaps surprisingly, lenses have seldom actually been used to implement updatable views in
databases. Bohannon, Pierce and Vaughan propose an approach to updatable views called relational lenses. However, to the best of our knowledge this
proposal has not been implemented or evaluated prior to the work reported in
this thesis.
This thesis proposes programming language support for relational lenses. Language integrated relational lenses support expressive and efficient view updates,
without relying on updatable view support from the database server. By integrating relational lenses into the programming language, application development
becomes easier and less error-prone, avoiding the impedance mismatch of having
two programming languages. Integrating relational lenses into the language poses
additional challenges. As defined by Bohannon et al. relational lenses completely
recompute the database, making them inefficient as the database scales. The
other challenge is that some parts of the well-formedness conditions are too general for implementation. Bohannon et al. specify predicates using possibly infinite
abstract sets and define the type checking rules using relational algebra.
Incremental relational lenses equip relational lenses with change-propagating semantics that map small changes to the view into (potentially) small changes
to the source tables. We prove that our incremental semantics are functionally
equivalent to the non-incremental semantics, and our experimental results show
orders of magnitude improvement over the non-incremental approach. This thesis introduces a concrete predicate syntax and shows how the required checks
are performed on these predicates and show that they satisfy the abstract predicate specifications. We discuss trade-offs between static predicates that are fully
known at compile time vs dynamic predicates that are only known during execution and introduce hybrid predicates taking inspiration from both approaches.
This thesis adapts the typing rules for relational lenses from sequential composition to a functional style of sub-expressions. We prove that any well-typed
functional relational lens expression can derive a well-typed sequential lens.
We use these additions to relational lenses as the foundation for two practical implementations: an extension of the Links functional language and a library written
in Haskell. The second implementation demonstrates how type-level computation can be used to implement relational lenses without changes to the compiler.
These two implementations attest to the possibility of turning relational lenses
into a practical language feature
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
The Diophantine problem in Chevalley groups
In this paper we study the Diophantine problem in Chevalley groups , where is an indecomposable root system of rank , is
an arbitrary commutative ring with . We establish a variant of double
centralizer theorem for elementary unipotents . This theorem is
valid for arbitrary commutative rings with . The result is principle to show
that any one-parametric subgroup , , is Diophantine
in . Then we prove that the Diophantine problem in is
polynomial time equivalent (more precisely, Karp equivalent) to the Diophantine
problem in . This fact gives rise to a number of model-theoretic corollaries
for specific types of rings.Comment: 44 page
Big in Reverse Mathematics: measure and category
The smooth development of large parts of mathematics hinges on the idea that
some sets are `small' or `negligible' and can therefore be ignored for a given
purpose. The perhaps most famous smallness notion, namely `measure zero',
originated with Lebesgue, while a second smallness notion, namely `meagre' or
`first category', originated with Baire around the same time. The associated
Baire category theorem is a central result governing the properties of meagre
(and related) sets, while the same holds for Tao's pigeonhole principle for
measure spaes and measure zero sets. In this paper, we study these theorems in
Kohlenbach's higher-order Reverse Mathematics, identifying a considerable
number of equivalent theorems. The latter involve most basic properties of
semi-continuous and pointwise discontinuous functions, Blumberg's theorem,
Riemann integration, and Volterra's early work circa 1881. All the
aforementioned theorems fall (far) outside of the Big Five of Reverse
Mathematics, and we investigate natural restrictions like Baire 1 and
quasi-continuity that make these theorems provable again in the Big Five (or
similar). Finally, despite the fundamental differences between measure and
category, the proofs of our equivalences turn out to be similar.Comment: 32 pages plus Technical Appendix. Same technical appendix as:
arXiv:2208.0302
- …