1,720,967 research outputs found
Music Analysis Through Mathematical Logic
No full textMusic and mathematics have a long-standing relationship, but what about music and logic? Only recently have some authors started to explore the relationship between logic and music analysis, thanks to developments in both fields. The aim of this paper is to analyze this relationship, by developing a system capable of analyzing chord sequences using a logical presentation as well as create new harmonic structures.
The logical presentation draws heavily from proof theory and its dual, i.e. tableuax. Also if music is not a proof, its adaptability makes it effective for this purpose. The attempt here proposed will try to apply proof theory to a brief, but important part of music: chord sequence analysi
Wittgenstein, Probability and Supraclassical Logics
No full textIn his Tractatus, Wittgenstein proposed a method for calculating probability using truth tables, which served as inspiration for Carnap and Ramsey's work on probability. Despite this, Wittgenstein's idea was not widely considered in the literature. This method involves comparing two propositions, where the first is considered only in true instances, while the other is analyzed only when the first is true. This approach is not dissimilar from Makinson's supraclassical logic, despite the use of different methods. The aim of this work is to shed light on Wittgenstein's method, exploring its foundational aspects and demonstrating the relationship between Wittgenstein's probability and Makinson's supraclassical logic. By doing so, we argue that Wittgenstein anticipated some modern developments in logic, proposing one of the earliest systems capable of incorporating beliefs within a formal calculus. In the final section, we will discuss how Wittgenstein's approach resolves (or, better, dissolves) the Lottery Paradox, showing that within this framework, the paradox ceases to exist
Essays in Network Economics
Get PDFNo abstract availableThe thesis is composed of 4 works. The first two concern production networks: the first chapter presents a model to analyse how the network shapes market power, the second is a study of the differences of a dynamic model of shock propagation with respect to a stylized static one. The last two concern diffusion of opinions rather than shocks: the third presents a model of joint diffusion of an epidemic state and opinions about the riskiness of an available immunization, modeled as cultural norms. The last is an analysis of a informational cascade model in the presence of overreaction, a well documented fact about agents, especially in financial settings
The social value of overreaction to information
No full textWe study the welfare effects of overreaction to information in markets with asymmetric information as well as the impact of a simple intervention in the form of a tax or a subsidy on trade volume. A large enough level of overreaction is always welfare decreasing: in these situations, introducing a tax can improve welfare. However, a small degree of overreaction can increase welfare. This is because of the interplay of two competing externalities: an information externality, due to the informational role of prices, and a pecuniary externality, due to the allocative role of prices. Depending on the balance of these externalities, a trade volume subsidy may be optimal
Foundations of LLCM : Labelled Lambek Calculus for Music Analysis
No full textThis paper presents an application of Lambek Calculus, a sequent calculus for categorial grammar, to music analysis. To this end, we propose a Labelled Lambek Calculus for Music (LLCM), where a label represents tonality information. In LLCM, each adjacent category represents a chord interpretation. When combined, they form a cadential category. We have enhanced the system with a rigorous and internally consistent framework that clarifies long-distance dependencies and provides a more explicit representation of relationships across different tonalities, including tonal shifts. A key innovation in LLCM is the introduction of a method for calculating the “depth” of a harmonic analysis. This measure corresponds to the complexity of chord progressions, enabling analysts to objectively compare different harmonic sequences based on their structural intricacy
A solution to the Lottery Paradox through Fractional Semantics
No full textThe Lockean Thesis and the Lottery Paradox have generated significant discussions within the context of classical logic. In this paper, we aim to provide a solution to this relationship by utilizing Fractional Semantics. The approach offered by Fractional Semantics is flexible enough to address the Lottery Paradox without using probability or non-classical logic. Instead, Fractional Semantics introduces a distinct type of semantics for Classical Logic, which proves to be an effective tool for resolving the paradox.
Using Fractional Semantics to solve the Lottery Paradox offers several benefits. First and foremost, it maintains the conjunction between beliefs while still utilizing Classical Logic. Furthermore, it allows for a more nuanced approach to the problem, offering greater insight into the nature of truth and falsehood within a belief system.
Our research demonstrates that Fractional Semantics provides a viable solution to the Lottery Paradox and highlights the value of considering different approaches to logical reasoning. By incorporating a more flexible and nuanced framework for understanding the nature of truth and belief, we can develop more effective strategies for addressing
complex problems in the real world
Belief Structures within Fractional Semantics : an overview
No full textHow can we reason effectively in social contexts marked by uncertainty, disagreement, and incomplete information? This volume explores foundational questions at the intersection of mathematical logic and social epistemology. It brings together contributions from philosophy, logic, computer science, and psychology, examining how individuals and groups revise beliefs, resolve conflicts, and make collective decisions. Most chapters stem from the 2023 workshop Reasoning with Imperfect Information in Social Settings, held at the Scuola Normale Superiore in Pisa. The volume shows how logical methods offer powerful, unifying tools for analyzing the dynamics of information exchange and public deliberation. In doing so, it makes a case for a rigorously formal and interdisciplinary approach to reasoning in complex social environments
Homophily and infections: Static and dynamic effects
Get PDFWe analyze the effect of homophily in the diffusion of a harmful state between two groups of agents that differ in immunization rates. Homophily has a very different impact on the steady state infection level (that is increasing in homophily when homophily is small, and decreasing when high), and on the cumulative number of infections generated by a deviation from the steady state (that, instead, is decreasing in homophily when homophily is small, and increasing when high). If immunization rates are endogenous, homophily has the opposite impact on the two groups. However, the sign of the group-level impact is the opposite if immunization is motivated by infection risk or peer pressure. If motivations are group-specific, homophily can be harmful to both groups
Third-party interest, resource value, and the likelihood of conflict
No full textResource wealth induces predation incentives but also conflict-deterring third-party involvement. As a result, the relation between resource value and conflict probability is a priori unclear. This paper studies such relation with a theoretical framework involving a potential aggressor and a powerful third party. First, we show that, if the third party’s incentives to intervene are sufficiently strong, conflict probability is hump-shaped in the resource value. Second, we theoretically establish that resource value increases the third party’s incentive to side with the resource-rich defendant in case of intervention, providing another mechanism for stabilization when the resource value is high. Third, we explain how our theory relates to policy-relevant case studies involving conflict-ridden areas (including inter-state or civil conflicts) and powerful third parties
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