Related papers: Localizing Finite-Depth Kripke Models
The Perfectly Transparent Equilibrium is algorithmically defined, for any game in normal form with perfect information and no ties, as the iterated deletion of non-individually-rational strategy profiles until at most one remains. In this…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…
We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract…
This is a short survey on the development of the formal specification and verification language H with emphasis on the scientific part. H is a modern highly expressive language solidly based upon advanced mathematical theories such as the…
We show that induction over $\Delta(\mathbb R)$-definable well-founded classes is equivalent to the reflection principle which asserts that any true formula of first order set theory with real parameters holds in some transitive set. The…
Presburger Arithmetic $\mathop{\mathbf{PrA}}\nolimits$ is the true theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for…
In their seminal paper Artemov and Protopopescu provide Hilbert formal systems, Brower-Heyting-Kolmogorov and Kripke semantics for the logics of intuitionistic belief and knowledge. Subsequently Krupski has proved that the logic of…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
Recursively defined linked data structures embedded in a pointer-based heap and their properties are naturally expressed in pure first-order logic with least fixpoint definitions (FO+lfp) with background theories. Such logics, unlike pure…
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central…
The main goal of this paper is to formulate a constructive analogue of Ackermann's observation about finite set theory and arithmetic. We will see that Heyting arithmetic is bi-interpretable with $\mathsf{CZF^{fin}}$, the finitary version…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
Prototype learning, a popular machine learning method designed for inherently interpretable decisions, leverages similarities to learned prototypes for classifying new data. While it is mainly applied in computer vision, in this work, we…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
This article reformulates the theory of computable physical models, previously introduced by the author, as a branch of applied model theory in first-order logic. It provides a semantic approach to the philosophy of science that…
We argue that it is logically possible to have a sort of both reality and locality in quantum mechanics. To demonstrate this, we construct a new quantitative model of hidden variables (HV's), dubbed solipsistic HV's, that interpolates…
In this paper we show how to introduce a conditional to Kripke's theory of truth that respects the deduction theorem for the consequence relation associated with the theory. To this effect we develop a novel supervaluational framework,…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…