Related papers: Type Theory in Ludics
This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.
We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
We provide a type theoretic treatment of the paper "On Tarski's fixed point theorem" by Giovanni Curi. There are benefits to having a type theoretic formulation apart from routine implementation in a proof assistant. By taking advantage of…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Factors are a foundational component of legal analysis and computational models of legal reasoning. These factor-based representations enable lawyers, judges, and AI and Law researchers to reason about legal cases. In this paper, we…
We present two Dialectica-like constructions for models of intensional Martin-L\"of type theory based on G\"odel's original Dialectica interpretation and the Diller-Nahm variant, bringing dependent types to categorical proof theory. We set…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
This paper introduces a space of variable lotteries and proves a constructive version of the expected utility theorem. The word ``constructive'' is used here in two senses. First, as in constructive mathematics, the logic underlying proofs…
The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…
It is conventional wisdom in machine learning and data mining that logical models such as rule sets are more interpretable than other models, and that among such rule-based models, simpler models are more interpretable than more complex…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…
The supercharacter theory of algebra groups gave us a representation theoretic realization of the Hopf algebra of symmetric functions in noncommuting variables. The underlying representation theoretic framework comes equipped with two…
The rules governing the essentially algebraic notion of a category with families have been observed (independently) by Steve Awodey and Marcelo Fiore to precisely match those of a representable natural transformation between presheaves.…
Propositional type theory, first studied by Henkin, is the restriction of simple type theory to a single base type that is interpreted as the set of the two truth values. We show that two constants (falsity and implication) suffice for…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…