Related papers: Mixed Logic and Storage Operators
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
In this paper, we consider modulation codes for practical multilevel flash memory storage systems with cell levels. Instead of maximizing the lifetime of the device [Ajiang-isit07-01, Ajiang-isit07-02, Yaakobi_verdy_siegel_wolf_allerton08,…
Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This type theory can be used as a metalanguage for synthetic guarded domain theory in which one can…
Large language models (LLMs) have demonstrated remarkable capabilities across a variety of tasks. One of the main challenges towards the successful deployment of LLMs is memory management, since they typically involve billions of…
Cirquent calculus is a new proof-theoretic and semantic approach introduced by G.Japaridze for the needs of his theory of computability logic. The earlier article "From formulas to cirquents in computability logic" by Japaridze generalized…
The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…
We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
Classical AI planners provide solutions to planning problems in the form of long and opaque text outputs. To aid in the understanding transferability of planning solutions, it is necessary to have a rich and comprehensible representation…
This paper provides an alternate characterization of type-two polynomial-time computability, with the goal of making second-order complexity theory more approachable. We rely on the usual oracle machines to model programs with subroutine…
The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful…
Decision-making under changing conditions remains a fundamental challenge in many real-world systems. Existing approaches often fail to generalize across shifting regimes and exhibit unstable behavior under uncertainty. This raises the…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
We investigate the combination of fragments of classical logic as a way of conservatively extending a given Boolean logic by the addition of new connectives, and we precisely characterize the circumstances in which such a combination…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
We study an assignment system of intersection types for a lambda-calculus with records and a record-merge operator, where types are preserved both under subject reduction and expansion. The calculus is expressive enough to naturally…
A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…
We present an adaptation, based on program extraction in elementary linear logic, of Krivine & Leivant's system FA_2. This system allows to write higher-order equations in order to specify the computational content of extracted programs.…
Effective caching is crucial for the performance of modern-day computing systems. A key optimization problem arising in caching -- which item to evict to make room for a new item -- cannot be optimally solved without knowing the future.…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing alternatives with decreasing degrees of preference in the heads of program rules. Despite the fact that the operational…