Related papers: One useful logic that defines its own truth
We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
The supervaluationist approach to fixed-point semantics is, arguably, the most celebrated and studied competitor to the Strong Kleene approach within Kripkean truth. In this paper, we show how to obtain supervaluationist fixed-point…
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum…
The four-valued semantics of Belnap--Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several non-classical logics depending on which feature of propositions we wish to preserve: truth, non-falsity,…
Existential rules form an expressive Datalog-based language to specify ontological knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the…
How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint…
A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of…