Related papers: A Forgotten Theory of Proofs ?
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation,…
The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
In the case of monotone independence, the transparent understanding of the mechanism to validate the central limit theorem (CLT) has been lacking, in sharp contrast to commutative, free and Boolean cases. We have succeeded in clarifying it…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
In this paper, we present a propositional logic (called mixed logic) containing disjoint copies of minimal, intuitionistic and classical logics. We prove a completeness theorem for this logic with respect to a Kripke semantics. We establish…
We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O'Hearn and Pym's logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave…
In this note we study a counterpart in predicate logic of the notion of 'logical friendliness', introduced into propositional logic in Makinson (2007). The result is a new consequence relation for predicate languages using first-order…
We provide the first (non-labelled) sequent calculi for bimodal provability logics with "usual" provability predicates. In particular, we introduce calculi for the logics CS, CSM and ER. Additionally, we present non-wellfounded versions of…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…
This paper investigates the logical strength of completeness theorems for modal propositional logic within second-order arithmetic. We demonstrate that the weak completeness theorem for modal propositional logic is provable in…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
We consider (finitary, propositional) logics through the original use of Category Theory: the study of the "sociology of mathematical objects", aligning us with a recent, and growing, trend of study logics through its relations with other…
Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof…
This letter introduces a new, substantially simplified version of the branching recurrence operation of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proves its equivalence to the old, "canonical" version.