Related papers: FMP for QD logics. A wrong proof
Poole has shown that nonmonotonic logics do not handle the lottery paradox correctly. In this paper we will show that Pollock's theory of defeasible reasoning fails for the same reason: defeasible reasoning is incompatible with the…
Quantum logic (QL) is a non-classical logic for analyzing the propositions of quantum physics. Modal logic MB, which is a logic that handles the value of the inner product that appears in quantum mechanics, was constructed with the…
In this talk, I try to show that the sign problem of dense QCD is due to modes whose frequency is higher than the chemical potential. An effective theory of quasi-quarks near the Fermi surface has a positive measure in the leading order.…
Many native ASP solvers exploit unfounded sets to compute consequences of a logic program via some form of well-founded negation, but disregard its contrapositive, well-founded justification (WFJ), due to computational cost. However, we…
We consider orthomodular posets endowed with a symmetric difference. We call them ODPs. Expressed in the quantum logic language, we consider quantum logics with an XOR-type connective. We study three classes of "almost Boolean" ODPs, two of…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…
Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness…
In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity. We investigate the Fitzpatrick extension of…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
It is a long-standing open problem whether modal logics of the form $\mathbf{K} \oplus \Box^n p \to \Box^m p$ for $n>m>1$ have the finite model property (FMP). We solve this by showing that any modal logic axiomatized by formulas of the…
Recently, with the application progress of AIGC tools based on large language models (LLMs), led by ChatGPT, many AI experts and more non-professionals are trumpeting the "reasoning ability" of the LLMs. The present author considers that…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.
Fuzzy Description Logics (DLs) are a family of logics which allow the representation of (and the reasoning with) structured knowledge affected by vagueness. Although most of the not very expressive crisp DLs, such as ALC, enjoy the Finite…
While state-of-the-art large language models (LLMs) demonstrate advanced reasoning capabilities-achieving remarkable performance on challenging competitive math and coding benchmarks-they also frequently fail on tasks that are easy for…
First-order temporal logics are notorious for their bad computational behaviour. It is known that even the two-variable monadic fragment is highly undecidable over various linear timelines, and over branching time even one-variable…