Related papers: The very dependent recursive structure of iterated…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into…
We investigate the partial orderings of the form (P(X),\subset), where X is a relational structure and P(X) the set of the domains of its isomorphic substructures. A rough classification of countable binary structures corresponding to the…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
This paper develops a version of dependent type theory in which isomorphism is handled through a direct generalization of the 1939 definitions of Bourbaki. More specifically we generalize the Bourbaki definition of structure from simple…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective; the semantics of this sort of implication is…
We define the continuous modeling property for first-order structures and show that a first-order structure has the continuous modelling property if and only if its age has the embedding Ramsey property. We use generalized indiscernible…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…
One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…