Related papers: The Flower Calculus
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…
Hybrid logic is a modal logic with additional operators specifying nominals and is highly expressive. For example, there is no formula corresponding to the irreflexivity of Kripke frames in basic modal logic, but there is in hybrid logic.…
We consider the following inference problem: Given a set of edge-flow signals observed on a graph, lift the graph to a cell complex, such that the observed edge-flow signals can be represented as a sparse combination of gradient and curl…
We present a calculus providing a Curry-Howard correspondence to classical logic represented in the sequent calculus with explicit structural rules, namely weakening and contraction. These structural rules introduce explicit erasure and…
Inspired by Bayesian approaches to brain function in neuroscience, we give a simple theory of probabilistic inference for a unified account of reasoning and learning. We simply model how data cause symbolic knowledge in terms of its…
A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
We introduce FIK, a natural intuitionistic modal logic specified by Kripke models satisfying the condition of forward confluence. We give a complete Hilbert-style axiomatization of this logic and propose a bi-nested calculus for it. The…
The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…
We introduce the notion of an ACP process algebra and the notion of a meadow enriched ACP process algebra. The former notion originates from the models of the axiom system ACP. The latter notion is a simple generalization of the former…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
We present the first formal correctness proof of Edmonds' blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and properties that allow the algorithm to run in…
Context: Edge graphs are graphs whose edges are labelled with identifiers, and nodes can have multiple edges between them. They are used to model a wide range of systems, including networks with distances or degrees of connection and…
We prove an analog of the flower theorem for non-degenerate reduced tangent to the identity germs that fix the coordinate hyperspaces in any dimension.
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…