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In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
Large language models (LLMs) achieve strong reasoning performance through chain-of-thought (CoT) reasoning, yet often generate unnecessarily long reasoning paths that incur high inference cost. Recent self-consistency-based approaches…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
While Chain-of-Thought (CoT) prompting boosts Language Models' (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We…
"Church's thesis" ($\mathsf{CT}$) as an axiom in constructive logic states that every total function of type $\mathbb{N} \to \mathbb{N}$ is computable, i.e. definable in a model of computation. $\mathsf{CT}$ is inconsistent in both…
Comparative constructions pose a challenge in Natural Language Inference (NLI), which is the task of determining whether a text entails a hypothesis. Comparatives are structurally complex in that they interact with other linguistic…
Large language models (LLMs) have rapidly progressed into general-purpose agents capable of solving a broad spectrum of tasks. However, current models remain inefficient at reasoning: they apply fixed inference-time compute regardless of…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
This paper proposes a formal framework for modeling the interaction of causal and (qualitative) epistemic reasoning. To this purpose, we extend the notion of a causal model with a representation of the epistemic state of an agent. On the…
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational…
We extend resource-bounded type theory to Martin-Lof type theory (MLTT) with dependent types, enabling size-indexed cost bounds for programs over inductive families. We introduce a resource-indexed universe hierarchy U_r where r is an…
This paper aims at comparing two coupling approaches as basic layers for building clustering criteria, suited for modularizing and clustering very large networks. We briefly use "optimal transport theory" as a starting point, and a way as…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
We introduce a new, substantially simplified version of the toggling-branching recurrence operation of Computability Logic, prove its equivalence to Japaridze's old, "canonical" version, and also prove that both versions preserve the static…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
Text-to-image (T2I) models enable rapid concept design, making them widely used in AI-driven design. While recent studies focus on generating semantic and stylistic variations of given design concepts, functional coherence--the integration…
Boney and Grossberg [BG] proved that every nice AEC has an independence relation. We prove that this relation is unique: In any given AEC, there can exist at most one independence relation that satisfies existence, extension, uniqueness and…