Related papers: A Proof-Theoretic Semantic Analysis of Dynamic Epi…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only…
The language of epistemic specifications and epistemic logic programs extends disjunctive logic programs under the stable model semantics with modal constructs called subjective literals. Using subjective literals, it is possible to check…
This paper proposes a basic proof theoretic framework for major modal logics: {\sf S5} and some of its subsystems. The framework is based on a version of hypersequent calculus, and the basic modal systems we handle here are the system {\sf…
G\"odel's Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to obtain the consistency of Peano arithmetic. In recent…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…
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…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…
Dynamic Epistemic Logic extends classical epistemic logic by modeling not only static knowledge but also its evolution through information updates. Among its various systems, Public Announcement Logic (PAL) provides one of the simplest and…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…