Related papers: FMP for QD logics. A wrong proof
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for…
The proof given in the paper was incomplete due to an omission in the proof of Lemma 2. A corrected and improved version of the paper is in arXiv:0902.2486.
This paper generalizes the 1977 paper of V.B. Shehtman, which constructed the first Kripke incomplete intermediate logic, by presenting a continuum of such logics. This version fixes an error in my simplified proof of incompleteness of…
Given a class of finite models we would like to expand each model (allowing new elements but the old universe is a separate sort), making the expressive power of LFP (least fix point logic) and PFP (inductive logic) similar while not…
In this article, the decidability and computability issues of dynamic probability logic (DPL) are addressed. Firstly, a proof system $\mathcal{H}_{DPL}$ is introduced for DPL and shown that it is weakly complete. Furthermore, this logic has…
We prove strong completeness results for some modal logics with the universal modality, with respect to their topological semantics over 0-dimensional dense-in-themselves metric spaces. We also use failure of compactness to show that, for…
Different notions of the consistency of obligations collapse in standard deontic logic. In justification logics, which feature explicit reasons for obligations, the situation is different. Their strength depends on a constant specification…
We address the problem of compiling defeasible theories to Datalog$^\neg$ programs. We prove the correctness of this compilation, for the defeasible logic $DL(\partial_{||})$, but the techniques we use apply to many other defeasible logics.…
Existing work investigates the reasoning capabilities of large language models (LLMs) to uncover their limitations, human-like biases and underlying processes. Such studies include evaluations of base LLMs (pre-trained on unlabeled corpora…
We introduce the logic QKSD which is a normal multi-modal logic over finitely many modalities that additionally supports bounded quantification of modalities. An important feature of this logic is that it allows to quantify over the…
Ultrafinitism postulates that we can only compute on relatively short objects, and numbers beyond certain value are not available. This approach would also forbid many forms of infinitary reasoning and allow to remove certain paradoxes…
State-of-the-art Large Language Models (LLMs) are accredited with an increasing number of different capabilities, ranging from reading comprehension, over advanced mathematical and reasoning skills to possessing scientific knowledge. In…
Fix a prime $p$. We prove that the set of sentences true in all but finitely many finite extensions of $\mathbb{Q}_p$ is undecidable in the language of valued fields with a cross-section. The proof goes via reduction to characteristic $p$,…
The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
The failure of Landau-Fermi liquid theory is often considered a telltale sign of universal, scale-invariant behavior in the emergent field theory of interacting fermions. Nevertheless, there exist borderline cases where weak scale…
This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
This paper provides a novel metametaphysical approach to quantum indeterminacy. More specifically, it argues that bivalent quantum logic can successfully account for this kind of indeterminacy, given the non-truth-functional character of…