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Multiplicative linear logic is a very well studied formal system, and most such studies are concerned with the one-sided sequent calculus. In this paper we look in detail at existing translations between a deep inference system and the…
The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together…
A predicate linear temporal logic LTL_{\lambda,=} without quantifiers but with predicate abstraction mechanism and equality is considered. The models of LTL_{\lambda,=} can be naturally seen as the systems of pebbles (flexible constants)…
The heterogeneity of tools that support temporal logic formulae poses several challenges in terms of interoperability. In particular, a standard syntax for temporal logic on finite traces, despite similar to the one for infinite traces, is…
Recent progress in deep reinforcement learning (DRL) can be largely attributed to the use of neural networks. However, this black-box approach fails to explain the learned policy in a human understandable way. To address this challenge and…
In this paper some proof theory for propositional Lax Logic is developed. A cut free terminating sequent calculus is introduced for the logic, and based on that calculus it is shown that the logic has uniform interpolation. Furthermore, a…
Dynamic topological logic ($\mathbf{DTL}$) is a trimodal logic designed for reasoning about dynamic topological systems. It was shown by Fern\'andez-Duque that the natural set of axioms for $\mathbf{DTL}$ is incomplete, but he provided a…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
Differential Linear Logic (DiLL) is a sequent calculus that expresses differentiation via symmetries between linear and non-linear formulas. In this paper, we express categorical models of DiLL as a pair of Grothendieck fibrations equipped…
Dynamic logic is a powerful framework for reasoning about imperative programs. An extension with a concurrent operator [18] was introduced to formalise programs running in parallel. In other direction, other authors proposed a systematic…
We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…
An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
In many real-life settings, agents must navigate dynamic environments while reasoning under incomplete information and acting on a corpus of unstable, context-dependent, and often conflicting norms. We introduce a general, non-modal,…
Answer substitutions play a central role in logic programming. To support {\it selective} answer substitutions, we refine $\exists x$ in goals into two different versions: the noisy version $\exists^o x$ and the silent version $\exists x$.…
We present a novel approach (DyNODE) that captures the underlying dynamics of a system by incorporating control in a neural ordinary differential equation framework. We conduct a systematic evaluation and comparison of our method and…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…