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The aim of this paper is to show that even if the natural algebraic semantic for modal (normal) logic is modal algebra, the more general class of subordination algebras (roughly speaking, the non symmetric contact algebras) is adequate too…
Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
Recent advances in Large Language Models (LLMs) have demonstrated the emergence of capabilities (learned skills) when the number of system parameters and the size of training data surpass certain thresholds. The exact mechanisms behind such…
The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges…
In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation,…
The structural balance of a signed graph is known to be necessary and sufficient to obtain a bipartite consensus among agents with friend-foe relationships. In the real world, relationships are multifarious, and the coexistence of different…
Currently, the variety of expressive extensions and different semantics created for logic programs with negation is diverse and heterogeneous, and there is a lack of comprehensive comparative studies which map out the multitude of…
We propose a new, structured, logic-based framework for legal reasoning and argumentation: Instead of using a single, unstructured meaning space, theory graphs organize knowledge and inference into collections of modular meaning spaces…
Causal graphs are commonly used to understand and model complex systems. Researchers often construct these graphs from different perspectives, leading to significant variations for the same problem. Comparing causal graphs is, therefore,…
Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are…
In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which…
Existing tools for explaining complex models and systems are associational rather than causal and do not provide mechanistic understanding. We propose a new notion called counterfactual explainability for causal attribution that is…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
For $g\ge 2$ and $n\ge 0$, let $\mathcal{H}_{g,n}\subset \mathcal{M}_{g,n}$ denote the complex moduli stack of $n$-marked smooth hyperelliptic curves of genus $g$. A normal crossings compactification of this space is provided by the theory…
Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
Frame semantic parsing is a semantic analysis task based on FrameNet which has received great attention recently. The task usually involves three subtasks sequentially: (1) target identification, (2) frame classification and (3) semantic…
This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…