Related papers: MALL proof equivalence is Logspace-complete, via b…
The log-rank conjecture is a longstanding open problem with multiple equivalent formulations in complexity theory and mathematics. In its linear-algebraic form, it asserts that the rank and partitioning number of a Boolean matrix are…
HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…
Despite their omnipresence in modern NLP, characterizing the computational power of transformer neural nets remains an interesting open question. We prove that transformers whose arithmetic precision is logarithmic in the number of input…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
We study the model checking problem, for fixed structures A, over positive equality-free first-order logic -- a natural generalisation of the non-uniform quantified constraint satisfaction problem QCSP(A). We prove a complete complexity…
We identify a subproblem of the model-checking problem for the epistemic \mu-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that…
We consider a problem that involves finding similar elements in a collection of sets. The problem is motivated by applications in machine learning and pattern recognition. We formulate the similar elements problem as an optimization and…
An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…
If two experts disagree on a test, we may conclude both cannot be 100 per cent correct. But if they completely agree, no possible evaluation can be excluded. This asymmetry in the utility of agreements versus disagreements is explored here…
Deciding the amalgamation property for a given class of finite structures is an important subroutine in classifying countable finitely homogeneous structures. We study the computational complexity of the amalgamation decision problem for…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…
Leveraging outputs from multiple large language models (LLMs) is emerging as a method for harnessing their power across a wide range of tasks while mitigating their capacity for making errors, e.g., hallucinations. However, current…
Abstract separation logics are a family of extensions of Hoare logic for reasoning about programs that manipulate resources such as memory locations. These logics are "abstract" because they are independent of any particular concrete…
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…
Logic programs P and Q are strongly equivalent if, given any program R, programs P union R and Q union R are equivalent (that is, have the same answer sets). Strong equivalence is convenient for the study of equivalent transformations of…
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit…
Linearizability and progress properties are key correctness notions for concurrent objects. However, model checking linearizability has suffered from the PSPACE-hardness of the trace inclusion problem. This paper proposes to exploit…