Related papers: A note on strong axiomatization of G\"odel Justifi…
In this paper we present various temporal justification logics involving both past and future time modalities. We combine Artemov's logic of proofs with linear temporal logic (with both past and future operators), and establish its…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
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…
Inclusion logic is a variant of dependence logic that was shown to have the same expressive power as positive greatest fixed-point logic. Inclusion logic is not axiomatizable in full, but its first-order consequences can be axiomatized. In…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We explore an inquisitive modal logic designed to reason about neighborhood models. This logic is based on an inquisitive strict conditional operator, which quantifies over neighborhoods, and which can be applied to both statements and…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
Holliday recently introduced a non-classical logic called Fundamental Logic, which intends to capture exactly those properties of the connectives "and", "or" and "not" that hold in virtue of their introduction and elimination rules in…
We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…
We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…
The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic…
Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $\exists y. \forall x. (\Box_x P(x,y) \supset\Diamond_y P(y,x))$. Like First order…
Non-additive uncertainty theories, typically possibility theory, belief functions and imprecise probabilities share a common feature with modal logic: the duality properties between possibility and necessity measures, belief and…
A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…
In medicine one frequently deals with vague information. As a tool for reasoning in this area, fuzzy logic suggests itself. In this paper we explore the applicability of the basic ideas of fuzzy set theory in the context of medical…
In the last years, the adoption of active systems has increased in many fields of computer science, such as databases, sensor networks, and software engineering. These systems are able to automatically react to events, by collecting…
We present a completeness result for a logical system which combines stit logic and justification logic in order to represent proving activity of the agents. This logic is interpreted over the semantics introduced in earlier publications.…