Related papers: Completeness for Two Left-Sequential Logics
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Recent advances in test-time scaling suggest that Large Language Models (LLMs) can gain better capabilities by generating Chain-of-Thought reasoning (analogous to human thinking) to respond a given request, and meanwhile exploring more…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on…
Starting from the observation that rational closure has the undesirable property of being an "all or nothing" mechanism, we here propose a multipreferential semantics, which enriches the preferential semantics underlying rational closure in…
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the…
The formal construction of the second-order logic or predicate calculus essentially adds quantifiers to propositional logic. Why second-order logic cannot be reduced to that of the first order? How to demonstrate that certain predicates are…
Recent advancements in large language models (LLMs) have significantly improved their reasoning abilities, particularly through techniques involving search and backtracking. Backtracking naturally scales test-time compute by enabling…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
Generating logical form equivalents of human language is a fresh way to employ neural architectures where long short-term memory effectively captures dependencies in both encoder and decoder units. The logical form of the sequence usually…
Step-by-step reasoning is widely used to enhance the reasoning ability of large language models (LLMs) in complex problems. Evaluating the quality of reasoning traces is crucial for understanding and improving LLM reasoning. However,…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for…
Large reasoning models (LRMs) generate complex reasoning traces with planning, reflection, verification, and backtracking. In this work, we introduce ReasoningFlow, a unified schema for analyzing the semantic structures of these complex…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
Program logics for bug-finding (such as the recently introduced Incorrectness Logic) have framed correctness and incorrectness as dual concepts requiring different logical foundations. In this paper, we argue that a single unified theory…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…