Related papers: Modal Functional (Dialectica) Interpretation
The interpretability logic of a mathematical theory describes the structural behavior of interpretations over that theory. Different theories have different logics. This paper from 2011 revolves around the question what logic describes the…
We investigate a recent proposal for modal hypersequent calculi. The interpretation of relational hypersequents incorporates an accessibility relation along the hypersequent. These systems give the same interpretation of hypersequents as…
We define a family of propositional constructive modal logics corresponding each to a different classical modal system. The logics are defined in the style of Wijesekera's constructive modal logic, and are both proof-theoretically and…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
We study the process of observation (measurement), within the framework of a `perspectival' (`relational', `relative state') version of the modal interpretation of quantum mechanics. We show that if we assume certain features of…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
The world is fundamentally compositional, so it is natural to think of visual recognition as the recognition of basic visually primitives that are composed according to well-defined rules. This strategy allows us to recognize unseen complex…
We generalize the theory of stable canonical rules by adopting definable filtration, a generalization of the method of filtration. We show that for a modal rule system or a modal logic that admits definable filtration, each extension is…
Despite the remarkable progress in neural models, their ability to generalize, a cornerstone for applications such as logical reasoning, remains a critical challenge. We delineate two fundamental aspects of this ability: compositionality,…
In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…
We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of…
We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…
This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: modal systems in which cognitive contexts extend known facts with hypothetical assumptions in order to explore their consequences.…