Related papers: A continuation semantics of interrogatives that ac…
The relationship between Lexical-Functional Grammar (LFG) {\em functional structures} (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that correctly explains…
One of the necessary extensions to the centering model is a mechanism to handle pronouns with intrasentential antecedents. Existing centering models deal only with discourses consisting of simple sentences. It leaves unclear how to delimit…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system…
In many expert and everyday reasoning contexts it is very useful to reason on the basis of defeasible assumptions. For instance, if the information at hand is incomplete we often use plausible assumptions, or if the information is…
We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…
We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as…
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…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…
We establish a correspondence between (fragments of) $\mathcal{TEL}^\bigcirc$, a temporal extension of the $\mathcal{EL}$ description logic with the LTL operator $\bigcirc^k$, and some specific kinds of formal grammars, in particular,…
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology-Based Query Answering. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure…
We observe that current conversational language models often waver in their judgments when faced with follow-up questions, even if the original judgment was correct. This wavering presents a significant challenge for generating reliable…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for…
B-terms are built from the B combinator alone defined by B f g x = f (g x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications…