1,217 research outputs found
Logical disagreement : an epistemological study
While the epistemic signiļ¬cance of disagreement has been a popular topic in epistemology for at least a decade, little attention has been paid to logical disagreement. This monograph is meant as a remedy. The text starts with an extensive literature review of the epistemology of (peer) disagreement and sets the stage for an epistemological study of logical disagreement. The guiding thread for the rest of the work is then three distinct readings of the ambiguous term ālogical disagreementā. Chapters 1 and 2 focus on the Ad Hoc Reading according to which logical disagreements occur when two subjects take incompatible doxastic attitudes toward a speciļ¬c proposition in or about logic. Chapter 2 presents a new counterexample to the widely discussed Uniqueness Thesis. Chapters 3 and 4 focus on the Theory Choice Reading of ālogical disagreementā. According to this interpretation, logical disagreements occur at the level of entire logical theories rather than individual entailment-claims. Chapter 4 concerns a key question from the philosophy of logic, viz., how we have epistemic justiļ¬cation for claims about logical consequence. In Chapters 5 and 6 we turn to the Akrasia Reading. On this reading, logical disagreements occur when there is a mismatch between the deductive strength of oneās background logic and the logical theory one prefers (oļ¬cially). Chapter 6 introduces logical akrasia by analogy to epistemic akrasia and presents a novel dilemma. Chapter 7 revisits the epistemology of peer disagreement and argues that the epistemic signiļ¬cance of central principles from the literature are at best deļ¬ated in the context of logical disagreement. The chapter also develops a simple formal model of deep disagreement in Default Logic, relating this to our general discussion of logical disagreement. The monograph ends in an epilogue with some reļ¬ections on the potential epistemic signiļ¬cance of convergence in logical theorizing
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
Polynomial time and dependent types
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one, based on the LFPL system of Martin Hofmann, that controls construction via a payment method. Both of these are extended to full dependent types via Quantitative Type Theory, allowing for arbitrary computation in types alongside guaranteed polynomial time computation in terms. We prove the soundness of the systems using a realisability technique due to Dal Lago and Hofmann. Our long-term goal is to combine the extensional reasoning of type theory with intensional reasoning about the resources intrinsically consumed by programs. This paper is a step along this path, which we hope will lead both to practical systems for reasoning about programsā resource usage, and to theoretical use as a form of synthetic computational complexity theory
Consistent Query Answering for Primary Keys on Rooted Tree Queries
We study the data complexity of consistent query answering (CQA) on databases
that may violate the primary key constraints. A repair is a maximal subset of
the database satisfying the primary key constraints. For a Boolean query q, the
problem CERTAINTY(q) takes a database as input, and asks whether or not each
repair satisfies q. The computational complexity of CERTAINTY(q) has been
established whenever q is a self-join-free Boolean conjunctive query, or a (not
necessarily self-join-free) Boolean path query. In this paper, we take one more
step towards a general classification for all Boolean conjunctive queries by
considering the class of rooted tree queries. In particular, we show that for
every rooted tree query q, CERTAINTY(q) is in FO, NL-hard LFP, or
coNP-complete, and it is decidable (in polynomial time), given q, which of the
three cases applies. We also extend our classification to larger classes of
queries with simple primary keys. Our classification criteria rely on query
homomorphisms and our polynomial-time fixpoint algorithm is based on a novel
use of context-free grammar (CFG).Comment: To appear in PODS'2
Collective agency:From philosophical and logical perspectives
People inhabit a vast and intricate social network nowadays. In addition to our own decisions and actions, we confront those of various groups every day. Collective decisions and actions are more complex and bewildering compared to those made by individuals. As members of a collective, we contribute to its decisions, but our contributions may not always align with the outcome. We may also find ourselves excluded from certain groups and passively subjected to their influences without being aware of the source. We are used to being in overlapping groups and may switch identities, supporting or opposing the claims of particular groups. But rarely do we pause to think: What do we talk about when we talk about groups and their decisions?At the heart of this dissertation is the question of collective agency, i.e., in what sense can we treat a group as a rational agent capable of its action. There are two perspectives we take: a philosophical and logical one. The philosophical perspective mainly discusses the ontological and epistemological issues related to collective agency, sorts out the relevant philosophical history, and argues that the combination of a relational view of collective agency and a dispositional view of collective intentionality provides a rational and realistic account. The logical perspective is associated with formal theories of groups, it disregards the psychological content involved in the philosophical perspective, establishes a logical system that is sufficiently formal and objective, and axiomatizes the nature of a collective
Calculus of Fractions for Quasicategories
We describe a generalization of Gabriel and Zisman's Calculus of Fractions to
quasicategories, showing that the two essentially coincide for the nerve of a
category. We then prove that the marked Ex-functor can be used to compute the
localization of a marked quasicategory satisfying our condition and that the
appropriate (co)completeness properties of the quasicategory carry over to its
localization. Finally, we present an application of these results to discrete
homotopy theory.Comment: 77 pages, comments welcom
Constraint Programming with External Worst-Case Traversal Time Analysis
peer reviewedThe allocation of software functions to processors under compute capacity and network links constraints is an important optimization problem in the field of embedded distributed systems. We present a hybrid approach to solve the allocation problem combining a constraint solver and a worst-case traversal time (WCTT) analysis that verifies the network timing constraints. The WCTT analysis is implemented as an industrial black-box program, which makes a tight integration with constraint solving challenging. We contribute to a new multi-objective constraint solving algorithm for integrating external under-approximating functions, such as the WCTT analysis, with constraint solving, and prove its correctness. We apply this new algorithm to the allocation problem in the context of automotive service-oriented architectures based on Ethernet networks, and provide a new dataset of realistic instances to evaluate our approach
Clones over Finite Sets and Minor Conditions
Achieving a classification of all clones of operations over a finite set is one of the goals at the heart of universal algebra. In 1921 Post provided a full description of the lattice of all clones over a two-element set. However, over the following years, it has been shown that a similar classification seems arduously reachable even if we only focus on clones over three-element sets: in 1959 Janov and MuÄnik proved that there exists a continuum of clones over a k-element set for every k > 2. Subsequent research in universal algebra therefore focused on understanding particular aspects of clone lattices over finite domains. Remarkable results in this direction are the description of maximal and minimal clones. One might still hope to classify all operation clones on finite domains up to some equivalence relation so that equivalent clones share many of the properties that are of interest in universal algebra.
In a recent turn of events, a weakening of the notion of clone homomorphism was introduced: a minor-preserving map from a clone C to D is a map which preserves arities and composition with projections. The minor-equivalence relation on clones over finite sets gained importance both in universal algebra and in computer science: minor-equivalent clones satisfy the same set identities of the form f(x_1,...,x_n) = g(y_1,...,y_m), also known as minor-identities. Moreover, it was proved that the complexity of the CSP of a finite structure A only depends on the set of minor-identities satisfied by the polymorphism clone of A. Throughout this dissertation we focus on the poset that arises by considering clones over a three-element set with the following order: we write C ā¤_{m} D if there exist a minor-preserving map from C to D. It has been proved that ā¤_{m} is a preorder; we call the poset arising from ā¤_{m} the pp-constructability poset.
We initiate a systematic study of the pp-constructability poset. To this end, we distinguish two cases that are qualitatively distinct: when considering clones over a finite set A, one can either set a boundary on the cardinality of A, or not. We denote by P_n the pp-constructability poset restricted to clones over a set A such that |A|=n and by P_{fin} we denote the whole pp-constructability poset, i.e., we only require A to be finite. First, we prove that P_{fin} is a semilattice and that it has no atoms. Moreover, we provide a complete description of P_2 and describe a significant part of P_3: we prove that P_3 has exactly three submaximal elements and present a full description of the ideal generated by one of these submaximal elements. As a byproduct, we prove that there are only countably many clones of self-dual operations over {0,1,2} up to minor-equivalence
Belief Revision in Expressive Knowledge Representation Formalisms
We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individualās competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence.
In belief revision area, the AGM postulates by AlchourrĆ³n, GƤrdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&Mās approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of ābaseā, such as belief sets, arbitrary or finite sets of sentences, or single sentences.
The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain āassignmentsā: functions mapping belief bases to total ā yet not transitive ā āpreferenceā relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&Mās original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach
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