Related papers: A note on strictly positive logics and word rewrit…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable…
Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
There are two kinds of approaches for termination analysis of logic programs: "transformational" and "direct" ones. Direct approaches prove termination directly on the basis of the logic program. Transformational approaches transform a…
We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as…
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a…
In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
The world's languages exhibit certain so-called typological or implicational universals; for example, Subject-Object-Verb (SOV) languages typically use postpositions. Explaining the source of such biases is a key goal of linguistics. We…
We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
To what extent can a neural network systematically reason over symbolic facts? Evidence suggests that large pre-trained language models (LMs) acquire some reasoning capacity, but this ability is difficult to control. Recently, it has been…