Related papers: The Discrete-Continuous Logic and its possible qua…
We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete…
Since its establishment, propositional dynamic logic (PDL) has been a subject of intensive academic research and frequent use in the industry. We have studied the complexity of some PDL problems and in this paper, we show results for some…
A persistent structural weakness in deep clustering is the disconnect between feature learning and cluster assignment. Most architectures invoke an external clustering step, typically k-means, to produce pseudo-labels that guide training,…
A skeleton of the category with finite coproducts D freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products C freely generated by a countable set of objects. As a consequence, we…
This paper presents a property of propositional theories under the answer sets semantics (called Equilibrium Logic for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly…
How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
We introduce proper display calculi for intuitionistic, bi-intuitionistic and classical linear logics with exponentials, which are sound, complete, conservative, and enjoy cut-elimination and subformula property. Based on the same design,…
It is shown that propositional calculuses of both quantum and classical logics are non-categorical. We find that quantum logic is in addition to an orthomodular lattice also modeled by a weakly orthomodular lattice and that classical logic…
In the propositional modal (and algebraic) treatment of two-variable first-order logic equality is modelled by a `diagonal' constant, interpreted in square products of universal frames as the identity (also known as the `diagonal')…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. In programming, short-circuit…
Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…
Description logics (DLs) are well-known knowledge representation formalisms focused on the representation of terminological knowledge. Due to their first-order semantics, these languages (in their classical form) are not suitable for…