相关论文: (Dual) Hoops Have Unique Halving

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…

In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…

Partial incorrectness logic (partial reverse Hoare logic) has recently been introduced as a new Hoare-style logic that over-approximates the weakest pre-conditions of a program and a post-condition. It is expected to verify systems where…

The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…

We study propositional logical systems arising from the language of Johansson's minimal logic and obtained by weakening the requirements for the negation operator. We present their semantics as a variant of neighbourhood semantics. We use…

Using coalgebraic methods, we extend Conway's theory of games to possibly non-terminating, i.e. non-wellfounded games (hypergames). We take the view that a play which goes on forever is a draw, and hence rather than focussing on winning…

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for…

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more…

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…

In this paper, we study logics of bounded distributive residuated lattices with modal operators considering $\Box$ and $\Diamond$ in a noncommutative setting. We introduce relational semantics for such substructural modal logics. We prove…

Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "t:",…

We find a translation with particularly nice properties from intuitionistic propositional logic in countably many variables to intuitionistic propositional logic in two variables. In addition, the existence of a possibly-not-as-nice…

Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

Interpolation is an important property of classical and many non classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the propositional version of the…

Propositional Dynamic Logic, PDL, is a modal logic designed to formalize the reasoning about programs. By extending accessibility between states to states and state sets, concurrent propositional dynamic logic CPDL, is introduced to include…

Let K be a variety of (commutative, integral) residuated lattices. The substructural logic usually associated with K is an algebraizable logic that has K as its equivalent algebraic semantics, and is a logic that preserves truth, i.e., 1 is…

In this work we present additional results related to the property of strong equivalence of logic programs. This property asserts that two programs share the same set of stable models, even under the addition of new rules. As shown in a…

The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions…