Related papers: Resolution in Linguistic Propositional Logic based…
We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability…
We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
Currently, there is a lack of rigorous theoretical system for systematically generating non-trivial and logically valid theorems. Addressing this critical gap, this paper conducts research to propose a novel automated theorem generation…
We show how to give a coherent semantics to programs that are well-specified in a version of separation logic for a language with higher types: idealized algol extended with heaps (but with immutable stack variables). In particular, we…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…
From an inconsistent database non-trivial arguments may be constructed both for a proposition, and for the contrary of that proposition. Therefore, inconsistency in a logical database causes uncertainty about which conclusions to accept.…
Sentential Calculus with Identity (SCI) is an extension of classical propositional logic, featuring a new connective of identity between formulas. In SCI two formulas are said to be identical if they share the same denotation. In the…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…
We discuss the syntax and semantics of relational Horn logic (RHL) and partial Horn logic (PHL). RHL is an extension of the Datalog programming language that allows introducing and equating variables in conclusions. PHL is a syntactic…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a semiring structure. PL is designed for complex quantitative…
The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work…