Related papers: The differential semantics of Lukasiewicz syntacti…
In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence $\phi$ according to this permutation…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
Stalnaker and Thomason famously proved that the conditional logic \textsf{C2} with first-order quantifiers is complete with respect to a selection function semantics. However, the selection functions used in this completeness result take…
It is demonstrated that under the hypothesis of boundedness, the semantics appears as a property of spontaneous physical processes. It turns that both semantic structure and semantic meaning have their own physical agents each of which is…
As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a $T-$periodic solution to the second order differential equation \begin{equation*} u"=\frac{h(t)}{u^{\lambda}} \end{equation*} are…
Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
A new $\theta$ function primitive is proposed that almost achieves the combined efficiency of the addition, multiplication and successor growth operations. This $\theta$ function symbol enables the constructing of an "IQFS(PA+)" axiom…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
Weak ontic necessity is the ontic necessity expressed by ``should'' or ``ought to'' in English. An example of it is ``I should be dead by now''. A feature of this necessity is whether it holds does not have anything to do with whether its…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
We study the finite element approximation of problems involving the weighted $\Phi$-Laplacian, where $\Phi$ is an $N$-function and the weight belongs to the class $A_\Phi$. In particular, we consider a boundary value problem and an obstacle…
Rigorous evaluation of the causal effects of semantic features on language model predictions can be hard to achieve for natural language reasoning problems. However, this is such a desirable form of analysis from both an interpretability…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…