Related papers: A Proof Procedure For Separation Logic With Induct…
We are interested in identifying and enforcing the isolation requirements of a concurrent program, i.e., concurrency control that ensures that the program meets its specification. The thesis of this paper is that this can be done…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
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…
The symbolic-heap fragment of separation logic has been actively developed and advocated for verifying the memory-safety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
Chain-of-Thought (CoT) prompting plays an indispensable role in endowing large language models (LLMs) with complex reasoning capabilities. However, CoT currently faces two fundamental challenges: (1) Sufficiency, which ensures that the…
A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a…
We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…
We investigate two problems for a class C of regular word languages. The C-membership problem asks for an algorithm to decide whether an input language belongs to C. The C-separation problem asks for an algorithm that, given as input two…
We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…