Related papers: Size Relationships in Abstract Cyclic Entailment S…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise…
We propose a general proof technique to show that a predicate is sound, that is, prevents stuck computation, with respect to a big-step semantics. This result may look surprising, since in big-step semantics there is no difference between…
The chase is a sound and complete algorithm for conjunctive query answering over ontologies of existential rules with equality. To enable its effective use, we can apply acyclicity notions; that is, sufficient conditions that guarantee…
Large language models (LLMs) are increasingly used in domains where causal reasoning matters, yet it remains unclear whether their judgments reflect normative causal computation, human-like shortcuts, or brittle pattern matching. We…
We define a class of Separation Logic formulae, whose entailment problem: given formulae $\phi, \psi_1, \ldots, \psi_n$, is every model of $\phi$ a model of some $\psi_i$? is 2EXPTIME-complete. The formulae in this class are existentially…
This paper analyzes the notion of causality in a conceptual model, mainly as applied in software engineering. Conceptual system modeling can be considered a three-level process that begins with building a static structural description to…
We propose a multi-scale extension of conformal prediction, an approach that constructs prediction sets with finite-sample coverage guarantees under minimal statistical assumptions. Classic conformal prediction relies on a single notion of…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
A simple finite-size scaling theory is proposed here for anisotropic percolation models considering the cluster size distribution function as generalized homogeneous function of the system size and two connectivity lengths. The proposed…
We propose a local model-checking proof system for a fragment of CTL. The rules of the proof system are motivated by the well-known fixed-point characterisation of CTL based on unfolding of the temporal operators. To guarantee termination…
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…
Size-Change Termination (SCT) is a method of proving program termination based on the impossibility of infinite descent. To this end we may use a program abstraction in which transitions are described by monotonicity constraints over…
We associate to every entanglement measure a family of measures which depend on a precision parameter, and which we call epsilon-measures of entanglement. Their definition aims at addressing a realistic scenario in which we need to estimate…
Brotherston and Simpson [citation] have formalized and investigated cyclic reasoning, reaching the important conclusion that it is at least as powerful as inductive reasoning (specifically, they showed that each inductive proof can be…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
We analyze the finite size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite size contributions to a general measure of ground state…