Related papers: Truth Predicate of Inductive Definitions and Logic…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
Completion is a well-known transformation that captures the stable model semantics of logic programs by turning a program into a set of first-order definitions. Stable models are models of the completion, but not all models of the…
Propositional dynamic logic (PDL) is presented in Sch\"{u}tte-style mode as one-sided semiformal tree-like sequent calculus Seq$_\omega^{\text{pdl}}$ with standard cut rule and the omega-rule with principal formulas $\left[ P^{\ast }\right]…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…
Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some…
In this paper the lightface $\Pi^{1}_{1}$-Comprehension axiom is shown to be proof-theoretically strong even over $\mbox{RCA}_{0}^{*}$, and we calibrate the proof-theoretic ordinals of weak fragments of the theory $\mbox{ID}_{1}$ of…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We introduce INDUCTION, a benchmark for finite structure concept synthesis in first order logic. Given small finite relational worlds with extensionally labeled target predicates, models must output a single first order logical formula that…
Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
This paper synthesizes a series of formal proofs to construct a unified theory on the logical limits of the Symbol Grounding Problem. We distinguish between internal meaning (sense), which formal systems can possess via axioms, and external…
Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of…
We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the…
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…