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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…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
We exhibit a 3-manifold which admits no tight contact structure.
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule…
We extend the linear {\pi}-calculus with composite regular types in such a way that data containing linear values can be shared among several processes, if there is no overlapping access to such values. We describe a type reconstruction…
A combinatorial model of molecular conformational space that was previously developped (J. Gabarro-Arpa, Comp. Biol. and Chem. 27, (2003) 153-159), had the drawback that structures could not be properly embedded beacause it lacked explicit…
We investigate the asymptotic number of elements of size $n$ in a particular class of closed lambda-terms (so-called $BCI(p)$-terms) which are related to axiom systems of combinatory logic. By deriving a differential equation for the…
We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any…
Counting the number of answers to conjunctive queries is a fundamental problem in databases that, under standard assumptions, does not have an efficient solution. The issue is inherently #P-hard, extending even to classes of acyclic…
This paper explores whether language models can effectively resolve the complex binding patterns of the Mandarin Chinese reflexive ziji, which are constrained by both syntactic and semantic factors. We construct a dataset of 240 synthetic…
In this paper we study the deductive properties of a family of 3-valued paraconsistent logics. We define a notion of standard sequent calculus and prove that there is no sound and complete standard sequent calculus for these logics.…
Bivariate generating functions for various subsets of the class of permutations containing no descending sequence of length three or more are determined. The notion of absolute indecomposability of a permutation is introduced, and used in…
Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise representational-system (RS) agnostic techniques that drive…
We study functional and concurrent calculi with non-determinism, along with type systems to control resources based on linearity. The interplay between non-determinism and linearity is delicate: careless handling of branches can discard…
Strict-Tolerant Logic (ST) underpins naive theories of truth and vagueness (respectively including a fully disquotational truth predicate and an unrestricted tolerance principle) without jettisoning any classically valid laws. The classical…
We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…
In linear regression problems with related predictors, it is desirable to do variable selection and estimation by maintaining the hierarchical or structural relationships among predictors. In this paper we propose non-negative garrote…